219.20/224.90 YES 219.20/224.90 219.20/224.90 Problem 1: 219.20/224.90 219.20/224.90 (VAR v_NonEmpty:S x1:S) 219.20/224.90 (RULES 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 ) 219.20/224.90 219.20/224.90 Problem 1: 219.20/224.90 219.20/224.90 Dependency Pairs Processor: 219.20/224.90 -> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(2(3(1(x1:S)))))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(2(2(3(1(x1:S))))) 219.20/224.90 0#(0(1(x1:S))) -> 1#(3(x1:S)) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 0#(4(0(4(x1:S)))) -> 0#(0(3(2(4(4(x1:S)))))) 219.20/224.90 0#(4(0(4(x1:S)))) -> 0#(3(2(4(4(x1:S))))) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(4(1(x1:S))) -> 0#(4(2(2(1(x1:S))))) 219.20/224.90 0#(4(1(x1:S))) -> 4#(2(2(1(x1:S)))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(3(2(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(0(3(2(1(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(0(3(1(x1:S)))) -> 4#(2(3(1(1(0(x1:S)))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 4#(2(1(1(2(1(x1:S)))))) 219.20/224.90 1#(4(1(x1:S))) -> 4#(2(1(1(x1:S)))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(2(3(3(1(4(x1:S)))))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 1#(3(0(4(x1:S)))) -> 0#(3(2(1(3(x1:S))))) 219.20/224.90 1#(3(0(4(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 1#(3(0(4(x1:S)))) -> 4#(0(3(2(1(3(x1:S)))))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(3(2(1(0(x1:S))))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 4#(0(3(2(1(0(x1:S)))))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 4#(3(2(0(0(1(x1:S)))))) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 0#(2(4(2(1(5(x1:S)))))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 4#(2(1(5(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(3(2(5(1(0(x1:S)))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(3(5(1(x1:S))))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(3(2(1(5(5(x1:S)))))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(5(1(x1:S)))) -> 5#(2(5(3(1(0(x1:S)))))) 219.20/224.90 5#(0(5(1(x1:S)))) -> 5#(3(1(0(x1:S)))) 219.20/224.90 5#(0(5(x1:S))) -> 0#(3(2(5(3(5(x1:S)))))) 219.20/224.90 5#(0(5(x1:S))) -> 5#(3(5(x1:S))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 0#(5(3(2(1(x1:S))))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 0#(3(5(2(2(1(x1:S)))))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 5#(2(2(1(x1:S)))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 5#(3(2(1(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(2(5(x1:S))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 1#(3(x1:S)) 219.20/224.90 5#(4(1(x1:S))) -> 4#(2(5(1(3(x1:S))))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 5#(4(3(1(x1:S)))) -> 4#(2(1(3(x1:S)))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 4#(2(1(x1:S))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 4#(3(2(1(x1:S)))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(2(4(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(2(4(3(2(1(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 1#(4(2(5(x1:S)))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 4#(2(5(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 -> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 219.20/224.90 Problem 1: 219.20/224.90 219.20/224.90 SCC Processor: 219.20/224.90 -> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(2(3(1(x1:S)))))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(2(2(3(1(x1:S))))) 219.20/224.90 0#(0(1(x1:S))) -> 1#(3(x1:S)) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 0#(4(0(4(x1:S)))) -> 0#(0(3(2(4(4(x1:S)))))) 219.20/224.90 0#(4(0(4(x1:S)))) -> 0#(3(2(4(4(x1:S))))) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(4(1(x1:S))) -> 0#(4(2(2(1(x1:S))))) 219.20/224.90 0#(4(1(x1:S))) -> 4#(2(2(1(x1:S)))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(3(2(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(0(3(2(1(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(0(3(1(x1:S)))) -> 4#(2(3(1(1(0(x1:S)))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 4#(2(1(1(2(1(x1:S)))))) 219.20/224.90 1#(4(1(x1:S))) -> 4#(2(1(1(x1:S)))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(2(3(3(1(4(x1:S)))))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 1#(3(0(4(x1:S)))) -> 0#(3(2(1(3(x1:S))))) 219.20/224.90 1#(3(0(4(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 1#(3(0(4(x1:S)))) -> 4#(0(3(2(1(3(x1:S)))))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(3(2(1(0(x1:S))))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 4#(0(3(2(1(0(x1:S)))))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 4#(3(2(0(0(1(x1:S)))))) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 0#(2(4(2(1(5(x1:S)))))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 4#(2(1(5(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(3(2(5(1(0(x1:S)))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(3(5(1(x1:S))))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(3(2(1(5(5(x1:S)))))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(5(1(x1:S)))) -> 5#(2(5(3(1(0(x1:S)))))) 219.20/224.90 5#(0(5(1(x1:S)))) -> 5#(3(1(0(x1:S)))) 219.20/224.90 5#(0(5(x1:S))) -> 0#(3(2(5(3(5(x1:S)))))) 219.20/224.90 5#(0(5(x1:S))) -> 5#(3(5(x1:S))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 0#(5(3(2(1(x1:S))))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 0#(3(5(2(2(1(x1:S)))))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 5#(2(2(1(x1:S)))) 219.20/224.90 5#(0(3(1(x1:S)))) -> 5#(3(2(1(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(2(5(x1:S))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 1#(3(x1:S)) 219.20/224.90 5#(4(1(x1:S))) -> 4#(2(5(1(3(x1:S))))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 5#(4(3(1(x1:S)))) -> 4#(2(1(3(x1:S)))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 4#(2(1(x1:S))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 4#(3(2(1(x1:S)))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(2(4(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(2(4(3(2(1(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 1#(4(2(5(x1:S)))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 4#(2(5(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 -> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 ->Strongly Connected Components: 219.20/224.90 ->->Cycle: 219.20/224.90 ->->-> Pairs: 219.20/224.90 1#(3(0(4(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 ->->-> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 ->->Cycle: 219.20/224.90 ->->-> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 ->->-> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 219.20/224.90 219.20/224.90 The problem is decomposed in 2 subproblems. 219.20/224.90 219.20/224.90 Problem 1.1: 219.20/224.90 219.20/224.90 Reduction Pair Processor: 219.20/224.90 -> Pairs: 219.20/224.90 1#(3(0(4(x1:S)))) -> 1#(3(x1:S)) 219.20/224.90 -> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 -> Usable rules: 219.20/224.90 Empty 219.20/224.90 ->Interpretation type: 219.20/224.90 Linear 219.20/224.90 ->Coefficients: 219.20/224.90 Natural Numbers 219.20/224.90 ->Dimension: 219.20/224.90 1 219.20/224.90 ->Bound: 219.20/224.90 2 219.20/224.90 ->Interpretation: 219.20/224.90 219.20/224.90 [0](X) = 2.X + 2 219.20/224.90 [4](X) = X + 2 219.20/224.90 [3](X) = 2.X 219.20/224.90 [1#](X) = 2.X 219.20/224.90 219.20/224.90 Problem 1.1: 219.20/224.90 219.20/224.90 SCC Processor: 219.20/224.90 -> Pairs: 219.20/224.90 Empty 219.20/224.90 -> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 ->Strongly Connected Components: 219.20/224.90 There is no strongly connected component 219.20/224.90 219.20/224.90 The problem is finite. 219.20/224.90 219.20/224.90 Problem 1.2: 219.20/224.90 219.20/224.90 Reduction Pair Processor: 219.20/224.90 -> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(0(1(x1:S))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 -> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 -> Usable rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 ->Interpretation type: 219.20/224.90 Linear 219.20/224.90 ->Coefficients: 219.20/224.90 Natural Numbers 219.20/224.90 ->Dimension: 219.20/224.90 1 219.20/224.90 ->Bound: 219.20/224.90 2 219.20/224.90 ->Interpretation: 219.20/224.90 219.20/224.90 [0](X) = 2.X + 1 219.20/224.90 [1](X) = X 219.20/224.90 [4](X) = X 219.20/224.90 [5](X) = X 219.20/224.90 [2](X) = X 219.20/224.90 [3](X) = X 219.20/224.90 [0#](X) = 2.X + 2 219.20/224.90 [1#](X) = X + 1 219.20/224.90 [4#](X) = X + 1 219.20/224.90 [5#](X) = X + 1 219.20/224.90 219.20/224.90 Problem 1.2: 219.20/224.90 219.20/224.90 SCC Processor: 219.20/224.90 -> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 -> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 ->Strongly Connected Components: 219.20/224.90 ->->Cycle: 219.20/224.90 ->->-> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 ->->-> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 219.20/224.90 Problem 1.2: 219.20/224.90 219.20/224.90 Reduction Pair Processor: 219.20/224.90 -> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.90 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.90 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.90 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 -> Rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 -> Usable rules: 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.90 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.90 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.90 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.90 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.90 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.90 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.90 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.90 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.90 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.90 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.90 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.90 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.90 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.90 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.90 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.90 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.90 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.90 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.90 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.90 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.90 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.90 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.90 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.90 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.90 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.90 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.90 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.90 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.90 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.90 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.90 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.90 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.90 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.90 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.90 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.90 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.90 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.90 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.90 ->Interpretation type: 219.20/224.90 Linear 219.20/224.90 ->Coefficients: 219.20/224.90 Natural Numbers 219.20/224.90 ->Dimension: 219.20/224.90 1 219.20/224.90 ->Bound: 219.20/224.90 2 219.20/224.90 ->Interpretation: 219.20/224.90 219.20/224.90 [0](X) = 2.X + 2 219.20/224.90 [1](X) = X 219.20/224.90 [4](X) = X 219.20/224.90 [5](X) = X 219.20/224.90 [2](X) = X 219.20/224.90 [3](X) = X 219.20/224.90 [0#](X) = 2.X + 2 219.20/224.90 [1#](X) = X 219.20/224.90 [4#](X) = X 219.20/224.90 [5#](X) = X 219.20/224.90 219.20/224.90 Problem 1.2: 219.20/224.90 219.20/224.90 SCC Processor: 219.20/224.90 -> Pairs: 219.20/224.90 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.90 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.90 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.90 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.90 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.90 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.90 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.90 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.90 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.90 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.90 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.90 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.90 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.90 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.90 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.90 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.90 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.90 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.90 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.90 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.90 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.90 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.90 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.90 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.90 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.90 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.90 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.90 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.90 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.90 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Strongly Connected Components: 219.20/224.91 ->->Cycle: 219.20/224.91 ->->-> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 ->->-> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 Reduction Pair Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(4(0(4(x1:S)))) -> 4#(4(x1:S)) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 -> Usable rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Interpretation type: 219.20/224.91 Linear 219.20/224.91 ->Coefficients: 219.20/224.91 Natural Numbers 219.20/224.91 ->Dimension: 219.20/224.91 1 219.20/224.91 ->Bound: 219.20/224.91 2 219.20/224.91 ->Interpretation: 219.20/224.91 219.20/224.91 [0](X) = 2.X + 2 219.20/224.91 [1](X) = X 219.20/224.91 [4](X) = X 219.20/224.91 [5](X) = X 219.20/224.91 [2](X) = X 219.20/224.91 [3](X) = X 219.20/224.91 [0#](X) = 2.X + 2 219.20/224.91 [1#](X) = X 219.20/224.91 [4#](X) = X 219.20/224.91 [5#](X) = X 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 SCC Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Strongly Connected Components: 219.20/224.91 ->->Cycle: 219.20/224.91 ->->-> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 ->->-> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 Reduction Pair Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 5#(1(1(x1:S))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 -> Usable rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Interpretation type: 219.20/224.91 Linear 219.20/224.91 ->Coefficients: 219.20/224.91 Natural Numbers 219.20/224.91 ->Dimension: 219.20/224.91 1 219.20/224.91 ->Bound: 219.20/224.91 2 219.20/224.91 ->Interpretation: 219.20/224.91 219.20/224.91 [0](X) = 2.X + 2 219.20/224.91 [1](X) = X 219.20/224.91 [4](X) = X 219.20/224.91 [5](X) = X 219.20/224.91 [2](X) = X 219.20/224.91 [3](X) = X 219.20/224.91 [0#](X) = 2.X + 2 219.20/224.91 [1#](X) = X 219.20/224.91 [4#](X) = X 219.20/224.91 [5#](X) = X 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 SCC Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Strongly Connected Components: 219.20/224.91 ->->Cycle: 219.20/224.91 ->->-> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 ->->-> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 Reduction Pair Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(2(1(3(x1:S)))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 -> Usable rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Interpretation type: 219.20/224.91 Linear 219.20/224.91 ->Coefficients: 219.20/224.91 Natural Numbers 219.20/224.91 ->Dimension: 219.20/224.91 1 219.20/224.91 ->Bound: 219.20/224.91 2 219.20/224.91 ->Interpretation: 219.20/224.91 219.20/224.91 [0](X) = 2.X + 1 219.20/224.91 [1](X) = X 219.20/224.91 [4](X) = X 219.20/224.91 [5](X) = X 219.20/224.91 [2](X) = X 219.20/224.91 [3](X) = X 219.20/224.91 [0#](X) = 2.X + 2 219.20/224.91 [1#](X) = X + 1 219.20/224.91 [4#](X) = X + 1 219.20/224.91 [5#](X) = X + 1 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 SCC Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Strongly Connected Components: 219.20/224.91 ->->Cycle: 219.20/224.91 ->->-> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 ->->-> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 Reduction Pair Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 -> Usable rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Interpretation type: 219.20/224.91 Linear 219.20/224.91 ->Coefficients: 219.20/224.91 Natural Numbers 219.20/224.91 ->Dimension: 219.20/224.91 1 219.20/224.91 ->Bound: 219.20/224.91 2 219.20/224.91 ->Interpretation: 219.20/224.91 219.20/224.91 [0](X) = 2.X + 2 219.20/224.91 [1](X) = X 219.20/224.91 [4](X) = X 219.20/224.91 [5](X) = X 219.20/224.91 [2](X) = X 219.20/224.91 [3](X) = X 219.20/224.91 [0#](X) = 2.X + 2 219.20/224.91 [1#](X) = X 219.20/224.91 [4#](X) = X 219.20/224.91 [5#](X) = X 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 SCC Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 -> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 ->Strongly Connected Components: 219.20/224.91 ->->Cycle: 219.20/224.91 ->->-> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.91 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.91 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.91 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.91 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.91 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.91 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.91 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.91 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.91 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.91 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.91 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.91 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.91 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.91 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.91 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.91 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.91 ->->-> Rules: 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.91 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.91 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.91 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.91 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.91 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.91 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.91 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.91 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.91 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.91 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.91 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.91 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.91 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.91 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.91 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.91 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.91 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.91 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.91 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.91 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.91 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.91 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.91 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.91 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.91 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.91 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.91 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.91 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.91 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.91 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.91 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.91 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.91 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.91 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.91 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.91 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.91 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.91 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.91 219.20/224.91 Problem 1.2: 219.20/224.91 219.20/224.91 Reduction Pair Processor: 219.20/224.91 -> Pairs: 219.20/224.91 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.91 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.91 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.91 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.91 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.91 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(2(x1:S))) 219.20/224.91 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.91 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.91 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.91 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.91 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.91 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.91 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 -> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 -> Usable rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 ->Interpretation type: 219.20/224.92 Linear 219.20/224.92 ->Coefficients: 219.20/224.92 Natural Numbers 219.20/224.92 ->Dimension: 219.20/224.92 1 219.20/224.92 ->Bound: 219.20/224.92 2 219.20/224.92 ->Interpretation: 219.20/224.92 219.20/224.92 [0](X) = X + 2 219.20/224.92 [1](X) = X 219.20/224.92 [4](X) = X 219.20/224.92 [5](X) = X 219.20/224.92 [2](X) = X 219.20/224.92 [3](X) = X 219.20/224.92 [0#](X) = X + 2 219.20/224.92 [1#](X) = X 219.20/224.92 [4#](X) = X 219.20/224.92 [5#](X) = X 219.20/224.92 219.20/224.92 Problem 1.2: 219.20/224.92 219.20/224.92 SCC Processor: 219.20/224.92 -> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 -> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 ->Strongly Connected Components: 219.20/224.92 ->->Cycle: 219.20/224.92 ->->-> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 ->->-> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 219.20/224.92 Problem 1.2: 219.20/224.92 219.20/224.92 Reduction Pair Processor: 219.20/224.92 -> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 -> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 -> Usable rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 ->Interpretation type: 219.20/224.92 Linear 219.20/224.92 ->Coefficients: 219.20/224.92 Natural Numbers 219.20/224.92 ->Dimension: 219.20/224.92 1 219.20/224.92 ->Bound: 219.20/224.92 2 219.20/224.92 ->Interpretation: 219.20/224.92 219.20/224.92 [0](X) = 2.X + 2 219.20/224.92 [1](X) = X 219.20/224.92 [4](X) = X 219.20/224.92 [5](X) = X 219.20/224.92 [2](X) = X 219.20/224.92 [3](X) = X 219.20/224.92 [0#](X) = 2.X + 2 219.20/224.92 [1#](X) = X 219.20/224.92 [4#](X) = X 219.20/224.92 [5#](X) = X 219.20/224.92 219.20/224.92 Problem 1.2: 219.20/224.92 219.20/224.92 SCC Processor: 219.20/224.92 -> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 -> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 ->Strongly Connected Components: 219.20/224.92 ->->Cycle: 219.20/224.92 ->->-> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 ->->-> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 219.20/224.92 Problem 1.2: 219.20/224.92 219.20/224.92 Reduction Pair Processor: 219.20/224.92 -> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(1(x1:S))) -> 1#(2(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 -> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 -> Usable rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 ->Interpretation type: 219.20/224.92 Linear 219.20/224.92 ->Coefficients: 219.20/224.92 Natural Numbers 219.20/224.92 ->Dimension: 219.20/224.92 1 219.20/224.92 ->Bound: 219.20/224.92 2 219.20/224.92 ->Interpretation: 219.20/224.92 219.20/224.92 [0](X) = 2.X + 2 219.20/224.92 [1](X) = X 219.20/224.92 [4](X) = X 219.20/224.92 [5](X) = X 219.20/224.92 [2](X) = X 219.20/224.92 [3](X) = X 219.20/224.92 [0#](X) = 2.X + 2 219.20/224.92 [1#](X) = X 219.20/224.92 [4#](X) = X 219.20/224.92 [5#](X) = X 219.20/224.92 219.20/224.92 Problem 1.2: 219.20/224.92 219.20/224.92 SCC Processor: 219.20/224.92 -> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 -> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 ->Strongly Connected Components: 219.20/224.92 ->->Cycle: 219.20/224.92 ->->-> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 ->->-> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 219.20/224.92 Problem 1.2: 219.20/224.92 219.20/224.92 Reduction Pair Processor: 219.20/224.92 -> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(1(x1:S)) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.20/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.20/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.20/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.20/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.20/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.20/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.20/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.20/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.20/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.20/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.20/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.20/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.20/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.20/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.20/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.20/224.92 -> Rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 -> Usable rules: 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.20/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.20/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.20/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.20/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.20/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.20/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.20/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.20/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.20/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.20/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.20/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.20/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.20/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.20/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.20/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.20/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.20/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.20/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.20/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.20/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.20/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.20/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.20/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.20/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.20/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.20/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.20/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.20/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.20/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.20/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.20/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.20/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.20/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.20/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.20/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.20/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.20/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.20/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.20/224.92 ->Interpretation type: 219.20/224.92 Linear 219.20/224.92 ->Coefficients: 219.20/224.92 Natural Numbers 219.20/224.92 ->Dimension: 219.20/224.92 1 219.20/224.92 ->Bound: 219.20/224.92 2 219.20/224.92 ->Interpretation: 219.20/224.92 219.20/224.92 [0](X) = 2.X + 2 219.20/224.92 [1](X) = X 219.20/224.92 [4](X) = X 219.20/224.92 [5](X) = X 219.20/224.92 [2](X) = X 219.20/224.92 [3](X) = X 219.20/224.92 [0#](X) = 2.X + 2 219.20/224.92 [1#](X) = X 219.20/224.92 [4#](X) = X 219.20/224.92 [5#](X) = X 219.20/224.92 219.20/224.92 Problem 1.2: 219.20/224.92 219.20/224.92 SCC Processor: 219.20/224.92 -> Pairs: 219.20/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.20/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.20/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.20/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.20/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.20/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.20/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.20/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.20/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.20/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.20/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.20/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.20/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.20/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.22/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 -> Rules: 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.92 ->Strongly Connected Components: 219.22/224.92 ->->Cycle: 219.22/224.92 ->->-> Pairs: 219.22/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.22/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 ->->-> Rules: 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.92 219.22/224.92 Problem 1.2: 219.22/224.92 219.22/224.92 Reduction Pair Processor: 219.22/224.92 -> Pairs: 219.22/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 0#(x1:S) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.22/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 -> Rules: 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.92 -> Usable rules: 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.92 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.92 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.92 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.92 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.92 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.92 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.92 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.92 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.92 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.92 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.92 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.92 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.92 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.92 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.92 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.92 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.92 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.92 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.92 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.92 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.92 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.92 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.92 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.92 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.92 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.92 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.92 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.92 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.92 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.92 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.92 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.92 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.92 ->Interpretation type: 219.22/224.92 Linear 219.22/224.92 ->Coefficients: 219.22/224.92 Natural Numbers 219.22/224.92 ->Dimension: 219.22/224.92 1 219.22/224.92 ->Bound: 219.22/224.92 2 219.22/224.92 ->Interpretation: 219.22/224.92 219.22/224.92 [0](X) = 2.X + 2 219.22/224.92 [1](X) = X 219.22/224.92 [4](X) = X 219.22/224.92 [5](X) = X 219.22/224.92 [2](X) = X 219.22/224.92 [3](X) = X 219.22/224.92 [0#](X) = 2.X + 2 219.22/224.92 [1#](X) = X 219.22/224.92 [4#](X) = X 219.22/224.92 [5#](X) = X 219.22/224.92 219.22/224.92 Problem 1.2: 219.22/224.92 219.22/224.92 SCC Processor: 219.22/224.92 -> Pairs: 219.22/224.92 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.92 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.92 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.92 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.92 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.92 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.92 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.92 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.92 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.92 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.92 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.92 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.92 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.92 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.92 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.92 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.92 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.92 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.92 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.92 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.92 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.22/224.92 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.92 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.92 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.92 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.92 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.92 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.92 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.92 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.92 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.92 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.92 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.92 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.92 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.92 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.92 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.92 -> Rules: 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.92 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.92 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.92 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.92 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.92 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.92 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Strongly Connected Components: 219.22/224.93 ->->Cycle: 219.22/224.93 ->->-> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 ->->-> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 Reduction Pair Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 1#(0(x1:S)) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 -> Usable rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Interpretation type: 219.22/224.93 Linear 219.22/224.93 ->Coefficients: 219.22/224.93 Natural Numbers 219.22/224.93 ->Dimension: 219.22/224.93 1 219.22/224.93 ->Bound: 219.22/224.93 2 219.22/224.93 ->Interpretation: 219.22/224.93 219.22/224.93 [0](X) = 2.X + 2 219.22/224.93 [1](X) = X 219.22/224.93 [4](X) = X 219.22/224.93 [5](X) = X 219.22/224.93 [2](X) = X 219.22/224.93 [3](X) = X 219.22/224.93 [0#](X) = 2.X + 2 219.22/224.93 [1#](X) = X 219.22/224.93 [4#](X) = X 219.22/224.93 [5#](X) = X 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 SCC Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Strongly Connected Components: 219.22/224.93 ->->Cycle: 219.22/224.93 ->->-> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 ->->-> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 Reduction Pair Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 1#(5(x1:S)) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 -> Usable rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Interpretation type: 219.22/224.93 Linear 219.22/224.93 ->Coefficients: 219.22/224.93 Natural Numbers 219.22/224.93 ->Dimension: 219.22/224.93 1 219.22/224.93 ->Bound: 219.22/224.93 2 219.22/224.93 ->Interpretation: 219.22/224.93 219.22/224.93 [0](X) = 2.X + 2 219.22/224.93 [1](X) = X 219.22/224.93 [4](X) = X 219.22/224.93 [5](X) = X 219.22/224.93 [2](X) = X 219.22/224.93 [3](X) = X 219.22/224.93 [0#](X) = 2.X + 2 219.22/224.93 [1#](X) = X 219.22/224.93 [4#](X) = X 219.22/224.93 [5#](X) = X 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 SCC Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Strongly Connected Components: 219.22/224.93 ->->Cycle: 219.22/224.93 ->->-> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 ->->-> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 Reduction Pair Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(0(5(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 -> Usable rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Interpretation type: 219.22/224.93 Linear 219.22/224.93 ->Coefficients: 219.22/224.93 Natural Numbers 219.22/224.93 ->Dimension: 219.22/224.93 1 219.22/224.93 ->Bound: 219.22/224.93 2 219.22/224.93 ->Interpretation: 219.22/224.93 219.22/224.93 [0](X) = 2.X + 2 219.22/224.93 [1](X) = X 219.22/224.93 [4](X) = X 219.22/224.93 [5](X) = X 219.22/224.93 [2](X) = X 219.22/224.93 [3](X) = X 219.22/224.93 [0#](X) = 2.X + 2 219.22/224.93 [1#](X) = X 219.22/224.93 [4#](X) = X 219.22/224.93 [5#](X) = X 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 SCC Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Strongly Connected Components: 219.22/224.93 ->->Cycle: 219.22/224.93 ->->-> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 ->->-> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 Reduction Pair Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 1#(x1:S) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 -> Usable rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Interpretation type: 219.22/224.93 Linear 219.22/224.93 ->Coefficients: 219.22/224.93 Natural Numbers 219.22/224.93 ->Dimension: 219.22/224.93 1 219.22/224.93 ->Bound: 219.22/224.93 2 219.22/224.93 ->Interpretation: 219.22/224.93 219.22/224.93 [0](X) = 2.X + 1 219.22/224.93 [1](X) = X 219.22/224.93 [4](X) = X 219.22/224.93 [5](X) = X 219.22/224.93 [2](X) = X 219.22/224.93 [3](X) = X 219.22/224.93 [0#](X) = 2.X + 2 219.22/224.93 [1#](X) = X + 1 219.22/224.93 [4#](X) = X + 1 219.22/224.93 [5#](X) = X + 1 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 SCC Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 ->Strongly Connected Components: 219.22/224.93 ->->Cycle: 219.22/224.93 ->->-> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 ->->-> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.93 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.93 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.93 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.93 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.93 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.93 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.93 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.93 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.93 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.93 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.93 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.93 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.93 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.93 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.93 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.93 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.93 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.93 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.93 219.22/224.93 Problem 1.2: 219.22/224.93 219.22/224.93 Reduction Pair Processor: 219.22/224.93 -> Pairs: 219.22/224.93 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.93 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.93 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.93 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.93 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.93 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.93 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.93 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.93 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.93 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.93 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.93 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.93 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.93 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.93 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.93 5#(0(0(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.93 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.93 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.93 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.93 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.93 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.93 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.93 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.93 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.93 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.93 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.93 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.93 -> Rules: 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.93 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.93 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.93 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.93 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.93 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.93 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.93 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.93 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.93 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.93 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.93 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.93 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.93 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.93 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.93 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.93 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.93 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.93 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.93 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.93 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 -> Usable rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 ->Interpretation type: 219.22/224.94 Linear 219.22/224.94 ->Coefficients: 219.22/224.94 Natural Numbers 219.22/224.94 ->Dimension: 219.22/224.94 1 219.22/224.94 ->Bound: 219.22/224.94 2 219.22/224.94 ->Interpretation: 219.22/224.94 219.22/224.94 [0](X) = 2.X + 2 219.22/224.94 [1](X) = X 219.22/224.94 [4](X) = X 219.22/224.94 [5](X) = X 219.22/224.94 [2](X) = X 219.22/224.94 [3](X) = X 219.22/224.94 [0#](X) = 2.X + 2 219.22/224.94 [1#](X) = X 219.22/224.94 [4#](X) = X 219.22/224.94 [5#](X) = X 219.22/224.94 219.22/224.94 Problem 1.2: 219.22/224.94 219.22/224.94 SCC Processor: 219.22/224.94 -> Pairs: 219.22/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.94 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.94 -> Rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 ->Strongly Connected Components: 219.22/224.94 ->->Cycle: 219.22/224.94 ->->-> Pairs: 219.22/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.94 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.94 ->->-> Rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 219.22/224.94 Problem 1.2: 219.22/224.94 219.22/224.94 Reduction Pair Processor: 219.22/224.94 -> Pairs: 219.22/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.94 5#(0(0(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.94 -> Rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 -> Usable rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 ->Interpretation type: 219.22/224.94 Linear 219.22/224.94 ->Coefficients: 219.22/224.94 Natural Numbers 219.22/224.94 ->Dimension: 219.22/224.94 1 219.22/224.94 ->Bound: 219.22/224.94 2 219.22/224.94 ->Interpretation: 219.22/224.94 219.22/224.94 [0](X) = 2.X + 2 219.22/224.94 [1](X) = X 219.22/224.94 [4](X) = X 219.22/224.94 [5](X) = X 219.22/224.94 [2](X) = X 219.22/224.94 [3](X) = X 219.22/224.94 [0#](X) = 2.X + 2 219.22/224.94 [1#](X) = X 219.22/224.94 [4#](X) = X 219.22/224.94 [5#](X) = X 219.22/224.94 219.22/224.94 Problem 1.2: 219.22/224.94 219.22/224.94 SCC Processor: 219.22/224.94 -> Pairs: 219.22/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.94 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.94 -> Rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 ->Strongly Connected Components: 219.22/224.94 ->->Cycle: 219.22/224.94 ->->-> Pairs: 219.22/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.94 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.94 ->->-> Rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.22/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.22/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.22/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.22/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.22/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.22/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.22/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.22/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.22/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.22/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.22/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.22/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.22/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.22/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.22/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.22/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.22/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.22/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.22/224.94 219.22/224.94 Problem 1.2: 219.22/224.94 219.22/224.94 Reduction Pair Processor: 219.22/224.94 -> Pairs: 219.22/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.22/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.22/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.22/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.22/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.22/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.22/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.22/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.22/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.22/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.22/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.22/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.22/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.22/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.22/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.22/224.94 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.22/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.22/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.22/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.22/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.22/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.22/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.22/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.22/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.22/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.22/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.22/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.22/224.94 -> Rules: 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.22/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.22/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.22/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.22/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.22/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.22/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.22/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.22/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.22/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.22/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.22/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.22/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.22/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.22/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.22/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.22/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.22/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.22/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.22/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.22/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 -> Usable rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 ->Interpretation type: 219.23/224.94 Linear 219.23/224.94 ->Coefficients: 219.23/224.94 Natural Numbers 219.23/224.94 ->Dimension: 219.23/224.94 1 219.23/224.94 ->Bound: 219.23/224.94 2 219.23/224.94 ->Interpretation: 219.23/224.94 219.23/224.94 [0](X) = 2.X + 2 219.23/224.94 [1](X) = X 219.23/224.94 [4](X) = X 219.23/224.94 [5](X) = X 219.23/224.94 [2](X) = X 219.23/224.94 [3](X) = X 219.23/224.94 [0#](X) = 2.X + 2 219.23/224.94 [1#](X) = X 219.23/224.94 [4#](X) = X 219.23/224.94 [5#](X) = X 219.23/224.94 219.23/224.94 Problem 1.2: 219.23/224.94 219.23/224.94 SCC Processor: 219.23/224.94 -> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 -> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 ->Strongly Connected Components: 219.23/224.94 ->->Cycle: 219.23/224.94 ->->-> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 ->->-> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 219.23/224.94 Problem 1.2: 219.23/224.94 219.23/224.94 Reduction Pair Processor: 219.23/224.94 -> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 1#(5(5(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 -> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 -> Usable rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 ->Interpretation type: 219.23/224.94 Linear 219.23/224.94 ->Coefficients: 219.23/224.94 Natural Numbers 219.23/224.94 ->Dimension: 219.23/224.94 1 219.23/224.94 ->Bound: 219.23/224.94 2 219.23/224.94 ->Interpretation: 219.23/224.94 219.23/224.94 [0](X) = 2.X + 2 219.23/224.94 [1](X) = X 219.23/224.94 [4](X) = X 219.23/224.94 [5](X) = X 219.23/224.94 [2](X) = X 219.23/224.94 [3](X) = X 219.23/224.94 [0#](X) = 2.X + 2 219.23/224.94 [1#](X) = X 219.23/224.94 [4#](X) = X 219.23/224.94 [5#](X) = X 219.23/224.94 219.23/224.94 Problem 1.2: 219.23/224.94 219.23/224.94 SCC Processor: 219.23/224.94 -> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 -> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 ->Strongly Connected Components: 219.23/224.94 ->->Cycle: 219.23/224.94 ->->-> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 ->->-> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 219.23/224.94 Problem 1.2: 219.23/224.94 219.23/224.94 Reduction Pair Processor: 219.23/224.94 -> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(1(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 -> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 -> Usable rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 ->Interpretation type: 219.23/224.94 Linear 219.23/224.94 ->Coefficients: 219.23/224.94 Natural Numbers 219.23/224.94 ->Dimension: 219.23/224.94 1 219.23/224.94 ->Bound: 219.23/224.94 2 219.23/224.94 ->Interpretation: 219.23/224.94 219.23/224.94 [0](X) = 2.X + 2 219.23/224.94 [1](X) = X 219.23/224.94 [4](X) = X 219.23/224.94 [5](X) = X 219.23/224.94 [2](X) = X 219.23/224.94 [3](X) = X 219.23/224.94 [0#](X) = 2.X + 2 219.23/224.94 [1#](X) = X 219.23/224.94 [4#](X) = X 219.23/224.94 [5#](X) = X 219.23/224.94 219.23/224.94 Problem 1.2: 219.23/224.94 219.23/224.94 SCC Processor: 219.23/224.94 -> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 -> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.94 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.94 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.94 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.94 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.94 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.94 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.94 ->Strongly Connected Components: 219.23/224.94 ->->Cycle: 219.23/224.94 ->->-> Pairs: 219.23/224.94 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.94 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.94 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.94 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.94 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.94 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.94 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.94 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.94 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.94 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.94 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.94 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.94 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.94 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.94 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.94 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.94 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.94 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.94 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.94 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.94 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.94 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.94 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.94 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.94 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.94 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.94 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.94 ->->-> Rules: 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.94 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.94 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.94 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.94 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.94 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.94 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.94 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.94 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.94 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.94 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.94 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.94 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.94 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.94 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.94 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.94 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.94 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.94 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.94 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.94 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.94 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.94 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.94 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.94 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.94 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.94 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.94 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.94 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.94 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.94 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.94 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.94 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 Reduction Pair Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(5(x1:S)) 219.23/224.95 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 -> Usable rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Interpretation type: 219.23/224.95 Linear 219.23/224.95 ->Coefficients: 219.23/224.95 Natural Numbers 219.23/224.95 ->Dimension: 219.23/224.95 1 219.23/224.95 ->Bound: 219.23/224.95 2 219.23/224.95 ->Interpretation: 219.23/224.95 219.23/224.95 [0](X) = 2.X + 2 219.23/224.95 [1](X) = X 219.23/224.95 [4](X) = X 219.23/224.95 [5](X) = X 219.23/224.95 [2](X) = X 219.23/224.95 [3](X) = X 219.23/224.95 [0#](X) = 2.X + 2 219.23/224.95 [1#](X) = X 219.23/224.95 [4#](X) = X 219.23/224.95 [5#](X) = X 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 SCC Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Strongly Connected Components: 219.23/224.95 ->->Cycle: 219.23/224.95 ->->-> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 ->->-> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 Reduction Pair Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 -> Usable rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Interpretation type: 219.23/224.95 Linear 219.23/224.95 ->Coefficients: 219.23/224.95 Natural Numbers 219.23/224.95 ->Dimension: 219.23/224.95 1 219.23/224.95 ->Bound: 219.23/224.95 2 219.23/224.95 ->Interpretation: 219.23/224.95 219.23/224.95 [0](X) = 2.X + 2 219.23/224.95 [1](X) = X 219.23/224.95 [4](X) = X 219.23/224.95 [5](X) = X 219.23/224.95 [2](X) = X 219.23/224.95 [3](X) = X 219.23/224.95 [0#](X) = 2.X + 2 219.23/224.95 [1#](X) = X 219.23/224.95 [4#](X) = X 219.23/224.95 [5#](X) = X 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 SCC Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Strongly Connected Components: 219.23/224.95 ->->Cycle: 219.23/224.95 ->->-> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 ->->-> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 Reduction Pair Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(2(1(5(x1:S)))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 -> Usable rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Interpretation type: 219.23/224.95 Linear 219.23/224.95 ->Coefficients: 219.23/224.95 Natural Numbers 219.23/224.95 ->Dimension: 219.23/224.95 1 219.23/224.95 ->Bound: 219.23/224.95 2 219.23/224.95 ->Interpretation: 219.23/224.95 219.23/224.95 [0](X) = 2.X + 2 219.23/224.95 [1](X) = X 219.23/224.95 [4](X) = X 219.23/224.95 [5](X) = X 219.23/224.95 [2](X) = X 219.23/224.95 [3](X) = X 219.23/224.95 [0#](X) = 2.X + 2 219.23/224.95 [1#](X) = X 219.23/224.95 [4#](X) = X 219.23/224.95 [5#](X) = X 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 SCC Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Strongly Connected Components: 219.23/224.95 ->->Cycle: 219.23/224.95 ->->-> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 ->->-> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 Reduction Pair Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 1#(5(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 -> Usable rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Interpretation type: 219.23/224.95 Linear 219.23/224.95 ->Coefficients: 219.23/224.95 Natural Numbers 219.23/224.95 ->Dimension: 219.23/224.95 1 219.23/224.95 ->Bound: 219.23/224.95 2 219.23/224.95 ->Interpretation: 219.23/224.95 219.23/224.95 [0](X) = 2.X + 2 219.23/224.95 [1](X) = X 219.23/224.95 [4](X) = X 219.23/224.95 [5](X) = X 219.23/224.95 [2](X) = X 219.23/224.95 [3](X) = X 219.23/224.95 [0#](X) = 2.X + 2 219.23/224.95 [1#](X) = X 219.23/224.95 [4#](X) = X 219.23/224.95 [5#](X) = X 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 SCC Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Strongly Connected Components: 219.23/224.95 ->->Cycle: 219.23/224.95 ->->-> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 ->->-> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 Reduction Pair Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(4(2(x1:S))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 -> Usable rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Interpretation type: 219.23/224.95 Linear 219.23/224.95 ->Coefficients: 219.23/224.95 Natural Numbers 219.23/224.95 ->Dimension: 219.23/224.95 1 219.23/224.95 ->Bound: 219.23/224.95 2 219.23/224.95 ->Interpretation: 219.23/224.95 219.23/224.95 [0](X) = 2.X + 1 219.23/224.95 [1](X) = X 219.23/224.95 [4](X) = X 219.23/224.95 [5](X) = X 219.23/224.95 [2](X) = X 219.23/224.95 [3](X) = X 219.23/224.95 [0#](X) = 2.X + 2 219.23/224.95 [1#](X) = X + 1 219.23/224.95 [4#](X) = X + 1 219.23/224.95 [5#](X) = X + 1 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 SCC Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 -> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 ->Strongly Connected Components: 219.23/224.95 ->->Cycle: 219.23/224.95 ->->-> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.95 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.95 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.95 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.95 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.95 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.95 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.95 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.95 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.95 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.95 ->->-> Rules: 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.95 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.95 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.95 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.95 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.95 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.95 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.95 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.95 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.95 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.95 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.95 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.95 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.95 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.95 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.95 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.95 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.95 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.95 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.95 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.95 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.95 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.95 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.95 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.95 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.95 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.95 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.95 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.95 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.95 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.95 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.95 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.95 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.95 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.95 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.95 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.95 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.95 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.95 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.95 219.23/224.95 Problem 1.2: 219.23/224.95 219.23/224.95 Reduction Pair Processor: 219.23/224.95 -> Pairs: 219.23/224.95 0#(0(1(x1:S))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.95 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.95 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.95 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.95 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.95 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.95 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.95 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.95 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.95 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.95 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.95 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.95 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.95 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.95 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.95 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.95 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 -> Usable rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Interpretation type: 219.23/224.96 Linear 219.23/224.96 ->Coefficients: 219.23/224.96 All rationals 219.23/224.96 ->Dimension: 219.23/224.96 1 219.23/224.96 ->Bound: 219.23/224.96 2 219.23/224.96 ->Interpretation: 219.23/224.96 219.23/224.96 [0](X) = X 219.23/224.96 [1](X) = 2.X + 2 219.23/224.96 [4](X) = 2.X 219.23/224.96 [5](X) = X + 1 219.23/224.96 [2](X) = 1/2.X 219.23/224.96 [3](X) = X 219.23/224.96 [0#](X) = X 219.23/224.96 [1#](X) = X + 1 219.23/224.96 [4#](X) = 2.X 219.23/224.96 [5#](X) = X 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 SCC Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Strongly Connected Components: 219.23/224.96 ->->Cycle: 219.23/224.96 ->->-> Pairs: 219.23/224.96 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 ->->-> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 Reduction Pair Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(1(2(0(x1:S)))) -> 0#(2(1(0(x1:S)))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 -> Usable rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Interpretation type: 219.23/224.96 Linear 219.23/224.96 ->Coefficients: 219.23/224.96 All rationals 219.23/224.96 ->Dimension: 219.23/224.96 1 219.23/224.96 ->Bound: 219.23/224.96 2 219.23/224.96 ->Interpretation: 219.23/224.96 219.23/224.96 [0](X) = 2.X 219.23/224.96 [1](X) = 2.X + 1 219.23/224.96 [4](X) = 2.X + 1/2 219.23/224.96 [5](X) = 2.X + 1/2 219.23/224.96 [2](X) = 1/2.X 219.23/224.96 [3](X) = X 219.23/224.96 [0#](X) = 1/2.X 219.23/224.96 [1#](X) = 1/2.X 219.23/224.96 [4#](X) = 1/2.X 219.23/224.96 [5#](X) = 1/2.X + 1 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 SCC Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Strongly Connected Components: 219.23/224.96 ->->Cycle: 219.23/224.96 ->->-> Pairs: 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 ->->-> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 Reduction Pair Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 0#(2(5(1(1(x1:S))))) 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 -> Usable rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Interpretation type: 219.23/224.96 Linear 219.23/224.96 ->Coefficients: 219.23/224.96 All rationals 219.23/224.96 ->Dimension: 219.23/224.96 1 219.23/224.96 ->Bound: 219.23/224.96 2 219.23/224.96 ->Interpretation: 219.23/224.96 219.23/224.96 [0](X) = 2.X 219.23/224.96 [1](X) = 2.X + 1 219.23/224.96 [4](X) = 2.X + 1 219.23/224.96 [5](X) = 2.X + 1/2 219.23/224.96 [2](X) = 1/2.X 219.23/224.96 [3](X) = X 219.23/224.96 [0#](X) = X + 1/2 219.23/224.96 [1#](X) = 1/2.X + 1 219.23/224.96 [4#](X) = X + 1 219.23/224.96 [5#](X) = X + 1/2 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 SCC Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Strongly Connected Components: 219.23/224.96 ->->Cycle: 219.23/224.96 ->->-> Pairs: 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 ->->-> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 Reduction Pair Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(5(4(1(1(x1:S))))) -> 4#(0(2(5(1(1(x1:S)))))) 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 -> Usable rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Interpretation type: 219.23/224.96 Linear 219.23/224.96 ->Coefficients: 219.23/224.96 All rationals 219.23/224.96 ->Dimension: 219.23/224.96 1 219.23/224.96 ->Bound: 219.23/224.96 2 219.23/224.96 ->Interpretation: 219.23/224.96 219.23/224.96 [0](X) = X 219.23/224.96 [1](X) = 2.X + 2 219.23/224.96 [4](X) = 2.X 219.23/224.96 [5](X) = X + 1 219.23/224.96 [2](X) = 1/2.X 219.23/224.96 [3](X) = X 219.23/224.96 [0#](X) = X + 1 219.23/224.96 [1#](X) = 2.X + 1 219.23/224.96 [4#](X) = 2.X + 1 219.23/224.96 [5#](X) = 2.X 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 SCC Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Strongly Connected Components: 219.23/224.96 ->->Cycle: 219.23/224.96 ->->-> Pairs: 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 ->->-> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 Reduction Pair Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 0#(0(3(x1:S))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 -> Usable rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Interpretation type: 219.23/224.96 Linear 219.23/224.96 ->Coefficients: 219.23/224.96 All rationals 219.23/224.96 ->Dimension: 219.23/224.96 1 219.23/224.96 ->Bound: 219.23/224.96 2 219.23/224.96 ->Interpretation: 219.23/224.96 219.23/224.96 [0](X) = 2.X 219.23/224.96 [1](X) = 2.X + 1 219.23/224.96 [4](X) = 2.X + 1/2 219.23/224.96 [5](X) = 2.X + 1/2 219.23/224.96 [2](X) = 1/2.X 219.23/224.96 [3](X) = X 219.23/224.96 [0#](X) = X + 1/2 219.23/224.96 [1#](X) = X 219.23/224.96 [4#](X) = X 219.23/224.96 [5#](X) = 1/2.X + 2 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 SCC Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 ->Strongly Connected Components: 219.23/224.96 ->->Cycle: 219.23/224.96 ->->-> Pairs: 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 ->->-> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 219.23/224.96 Problem 1.2: 219.23/224.96 219.23/224.96 Reduction Pair Processor: 219.23/224.96 -> Pairs: 219.23/224.96 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.96 0#(3(4(0(x1:S)))) -> 4#(0(0(3(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.96 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.96 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.96 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.96 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.96 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.96 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.96 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.96 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.96 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.96 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.96 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.96 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.96 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.96 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.96 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.96 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.96 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.96 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.96 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.96 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.96 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.96 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.96 -> Rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.96 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.96 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.96 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.96 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.96 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.96 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.96 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.96 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.96 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.96 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.96 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.96 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.96 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.96 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.96 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.96 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.96 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.96 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.96 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.96 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.96 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.96 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.96 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.96 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.96 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.96 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.96 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.96 -> Usable rules: 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.96 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.96 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.96 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.96 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.96 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.96 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.96 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.96 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.96 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.96 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.96 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Interpretation type: 219.23/224.97 Linear 219.23/224.97 ->Coefficients: 219.23/224.97 All rationals 219.23/224.97 ->Dimension: 219.23/224.97 1 219.23/224.97 ->Bound: 219.23/224.97 2 219.23/224.97 ->Interpretation: 219.23/224.97 219.23/224.97 [0](X) = 2.X 219.23/224.97 [1](X) = 2.X + 2 219.23/224.97 [4](X) = 2.X + 1 219.23/224.97 [5](X) = X + 1/2 219.23/224.97 [2](X) = 1/2.X 219.23/224.97 [3](X) = X 219.23/224.97 [0#](X) = 1/2.X + 1/2 219.23/224.97 [1#](X) = 1/2.X + 1 219.23/224.97 [4#](X) = 1/2.X + 1/2 219.23/224.97 [5#](X) = 1/2.X 219.23/224.97 219.23/224.97 Problem 1.2: 219.23/224.97 219.23/224.97 SCC Processor: 219.23/224.97 -> Pairs: 219.23/224.97 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 0#(x1:S) 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(1(x1:S))) -> 0#(2(1(1(2(x1:S))))) 219.23/224.97 1#(0(1(x1:S))) -> 0#(2(1(1(x1:S)))) 219.23/224.97 1#(0(3(1(x1:S)))) -> 0#(x1:S) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S))) 219.23/224.97 4#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 0#(2(1(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 0#(2(1(x1:S))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 0#(x1:S) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 0#(0(2(1(5(x1:S))))) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 0#(2(1(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 0#(2(5(4(2(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Strongly Connected Components: 219.23/224.97 ->->Cycle: 219.23/224.97 ->->-> Pairs: 219.23/224.97 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.97 ->->-> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->->Cycle: 219.23/224.97 ->->-> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 ->->-> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 219.23/224.97 219.23/224.97 The problem is decomposed in 2 subproblems. 219.23/224.97 219.23/224.97 Problem 1.2.1: 219.23/224.97 219.23/224.97 Reduction Pair Processor: 219.23/224.97 -> Pairs: 219.23/224.97 0#(2(0(1(x1:S)))) -> 0#(0(2(1(3(x1:S))))) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 -> Usable rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Interpretation type: 219.23/224.97 Linear 219.23/224.97 ->Coefficients: 219.23/224.97 All rationals 219.23/224.97 ->Dimension: 219.23/224.97 1 219.23/224.97 ->Bound: 219.23/224.97 2 219.23/224.97 ->Interpretation: 219.23/224.97 219.23/224.97 [0](X) = 1/2.X 219.23/224.97 [1](X) = 2 219.23/224.97 [4](X) = 2 219.23/224.97 [5](X) = 2.X + 1/2 219.23/224.97 [2](X) = 1/2 219.23/224.97 [3](X) = 0 219.23/224.97 [0#](X) = 1/2.X 219.23/224.97 219.23/224.97 Problem 1.2.1: 219.23/224.97 219.23/224.97 SCC Processor: 219.23/224.97 -> Pairs: 219.23/224.97 Empty 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Strongly Connected Components: 219.23/224.97 There is no strongly connected component 219.23/224.97 219.23/224.97 The problem is finite. 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 Reduction Pair Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(1(4(0(x1:S)))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 -> Usable rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Interpretation type: 219.23/224.97 Linear 219.23/224.97 ->Coefficients: 219.23/224.97 All rationals 219.23/224.97 ->Dimension: 219.23/224.97 1 219.23/224.97 ->Bound: 219.23/224.97 2 219.23/224.97 ->Interpretation: 219.23/224.97 219.23/224.97 [0](X) = 2.X 219.23/224.97 [1](X) = 2.X + 2 219.23/224.97 [4](X) = 2.X + 1 219.23/224.97 [5](X) = X + 1/2 219.23/224.97 [2](X) = 1/2.X 219.23/224.97 [3](X) = X 219.23/224.97 [1#](X) = 2.X + 1/2 219.23/224.97 [4#](X) = 2.X + 2 219.23/224.97 [5#](X) = 2.X 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 SCC Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Strongly Connected Components: 219.23/224.97 ->->Cycle: 219.23/224.97 ->->-> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 ->->-> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 Reduction Pair Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 1#(4(0(x1:S))) 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 -> Usable rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Interpretation type: 219.23/224.97 Linear 219.23/224.97 ->Coefficients: 219.23/224.97 All rationals 219.23/224.97 ->Dimension: 219.23/224.97 1 219.23/224.97 ->Bound: 219.23/224.97 2 219.23/224.97 ->Interpretation: 219.23/224.97 219.23/224.97 [0](X) = 2.X 219.23/224.97 [1](X) = 2.X + 2 219.23/224.97 [4](X) = 2.X + 1 219.23/224.97 [5](X) = 2.X + 1/2 219.23/224.97 [2](X) = 1/2.X 219.23/224.97 [3](X) = X 219.23/224.97 [1#](X) = 1/2.X + 1/2 219.23/224.97 [4#](X) = X + 1 219.23/224.97 [5#](X) = X 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 SCC Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Strongly Connected Components: 219.23/224.97 ->->Cycle: 219.23/224.97 ->->-> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 ->->-> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 Reduction Pair Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(1(4(x1:S)))) -> 4#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 -> Usable rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Interpretation type: 219.23/224.97 Linear 219.23/224.97 ->Coefficients: 219.23/224.97 All rationals 219.23/224.97 ->Dimension: 219.23/224.97 1 219.23/224.97 ->Bound: 219.23/224.97 2 219.23/224.97 ->Interpretation: 219.23/224.97 219.23/224.97 [0](X) = 2.X 219.23/224.97 [1](X) = 2.X + 1 219.23/224.97 [4](X) = 2.X + 1/2 219.23/224.97 [5](X) = 2.X + 1/2 219.23/224.97 [2](X) = 1/2.X 219.23/224.97 [3](X) = X 219.23/224.97 [1#](X) = X + 2 219.23/224.97 [4#](X) = X + 2 219.23/224.97 [5#](X) = 2.X + 1 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 SCC Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Strongly Connected Components: 219.23/224.97 ->->Cycle: 219.23/224.97 ->->-> Pairs: 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 ->->-> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 Reduction Pair Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 -> Usable rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Interpretation type: 219.23/224.97 Linear 219.23/224.97 ->Coefficients: 219.23/224.97 All rationals 219.23/224.97 ->Dimension: 219.23/224.97 1 219.23/224.97 ->Bound: 219.23/224.97 2 219.23/224.97 ->Interpretation: 219.23/224.97 219.23/224.97 [0](X) = 2.X 219.23/224.97 [1](X) = 2.X + 1 219.23/224.97 [4](X) = 2.X + 1/2 219.23/224.97 [5](X) = 2.X + 1/2 219.23/224.97 [2](X) = 1/2.X 219.23/224.97 [3](X) = X 219.23/224.97 [1#](X) = 2.X + 1 219.23/224.97 [4#](X) = 2.X + 2 219.23/224.97 [5#](X) = 2.X 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 SCC Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Strongly Connected Components: 219.23/224.97 ->->Cycle: 219.23/224.97 ->->-> Pairs: 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 ->->-> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 Reduction Pair Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(0(3(1(x1:S)))) -> 1#(1(0(x1:S))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 -> Usable rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.97 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.97 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.97 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.97 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.97 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.97 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.97 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.97 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.97 ->Interpretation type: 219.23/224.97 Linear 219.23/224.97 ->Coefficients: 219.23/224.97 All rationals 219.23/224.97 ->Dimension: 219.23/224.97 1 219.23/224.97 ->Bound: 219.23/224.97 2 219.23/224.97 ->Interpretation: 219.23/224.97 219.23/224.97 [0](X) = 2.X 219.23/224.97 [1](X) = 2.X + 1 219.23/224.97 [4](X) = 2.X + 1/2 219.23/224.97 [5](X) = 2.X + 1/2 219.23/224.97 [2](X) = 1/2.X 219.23/224.97 [3](X) = X 219.23/224.97 [1#](X) = X 219.23/224.97 [4#](X) = X + 1/2 219.23/224.97 [5#](X) = 1/2.X + 2 219.23/224.97 219.23/224.97 Problem 1.2.2: 219.23/224.97 219.23/224.97 SCC Processor: 219.23/224.97 -> Pairs: 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.97 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.97 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.97 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.97 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.97 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.97 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.97 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.97 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.97 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.97 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.97 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.97 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.97 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.97 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.97 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.97 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.97 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.97 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.97 -> Rules: 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.97 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.97 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.97 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.97 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.97 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.97 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.97 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.97 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.97 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.97 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.97 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.97 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.97 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.97 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.97 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.97 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.97 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.97 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.97 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.97 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.97 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.97 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.97 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.97 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.97 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.97 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.97 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.97 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.97 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.97 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Strongly Connected Components: 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.98 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 Reduction Pair Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 1#(4(x1:S)) 219.23/224.98 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 -> Usable rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Interpretation type: 219.23/224.98 Linear 219.23/224.98 ->Coefficients: 219.23/224.98 All rationals 219.23/224.98 ->Dimension: 219.23/224.98 1 219.23/224.98 ->Bound: 219.23/224.98 2 219.23/224.98 ->Interpretation: 219.23/224.98 219.23/224.98 [0](X) = X 219.23/224.98 [1](X) = 2.X + 2 219.23/224.98 [4](X) = 2.X 219.23/224.98 [5](X) = X + 1 219.23/224.98 [2](X) = 1/2.X 219.23/224.98 [3](X) = X 219.23/224.98 [1#](X) = 1/2.X + 2 219.23/224.98 [4#](X) = X + 1/2 219.23/224.98 [5#](X) = 1/2.X + 1/2 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 SCC Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Strongly Connected Components: 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 Reduction Pair Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 1#(2(5(1(4(x1:S))))) 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 -> Usable rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Interpretation type: 219.23/224.98 Linear 219.23/224.98 ->Coefficients: 219.23/224.98 All rationals 219.23/224.98 ->Dimension: 219.23/224.98 1 219.23/224.98 ->Bound: 219.23/224.98 2 219.23/224.98 ->Interpretation: 219.23/224.98 219.23/224.98 [0](X) = X 219.23/224.98 [1](X) = 2.X + 2 219.23/224.98 [4](X) = 2.X 219.23/224.98 [5](X) = 2.X + 1 219.23/224.98 [2](X) = 1/2.X 219.23/224.98 [3](X) = X 219.23/224.98 [1#](X) = X 219.23/224.98 [4#](X) = X 219.23/224.98 [5#](X) = X + 1/2 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 SCC Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Strongly Connected Components: 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 Reduction Pair Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 4#(x1:S) 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 -> Usable rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Interpretation type: 219.23/224.98 Linear 219.23/224.98 ->Coefficients: 219.23/224.98 All rationals 219.23/224.98 ->Dimension: 219.23/224.98 1 219.23/224.98 ->Bound: 219.23/224.98 2 219.23/224.98 ->Interpretation: 219.23/224.98 219.23/224.98 [0](X) = 2.X 219.23/224.98 [1](X) = 2.X + 2 219.23/224.98 [4](X) = 2.X + 2 219.23/224.98 [5](X) = X + 1/2 219.23/224.98 [2](X) = 1/2.X 219.23/224.98 [3](X) = X 219.23/224.98 [1#](X) = X 219.23/224.98 [4#](X) = X 219.23/224.98 [5#](X) = 1/2.X 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 SCC Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Strongly Connected Components: 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 Reduction Pair Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(5(x1:S)))) -> 5#(1(4(x1:S))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 -> Usable rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Interpretation type: 219.23/224.98 Linear 219.23/224.98 ->Coefficients: 219.23/224.98 All rationals 219.23/224.98 ->Dimension: 219.23/224.98 1 219.23/224.98 ->Bound: 219.23/224.98 2 219.23/224.98 ->Interpretation: 219.23/224.98 219.23/224.98 [0](X) = 2.X 219.23/224.98 [1](X) = 2.X + 1 219.23/224.98 [4](X) = 2.X + 1 219.23/224.98 [5](X) = 2.X + 1/2 219.23/224.98 [2](X) = 1/2.X 219.23/224.98 [3](X) = X 219.23/224.98 [1#](X) = X + 2 219.23/224.98 [4#](X) = X + 2 219.23/224.98 [5#](X) = 2.X 219.23/224.98 219.23/224.98 Problem 1.2.2: 219.23/224.98 219.23/224.98 SCC Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(0(5(1(x1:S)))) -> 1#(0(x1:S)) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(5(4(2(5(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 1#(x1:S) 219.23/224.98 5#(4(1(5(x1:S)))) -> 4#(5(5(2(1(x1:S))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Strongly Connected Components: 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.98 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.98 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.98 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.98 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.98 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.98 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.98 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 219.23/224.98 219.23/224.98 The problem is decomposed in 2 subproblems. 219.23/224.98 219.23/224.98 Problem 1.2.2.1: 219.23/224.98 219.23/224.98 Reduction Pair Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(2(1(x1:S)))) 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 -> Usable rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Interpretation type: 219.23/224.98 Linear 219.23/224.98 ->Coefficients: 219.23/224.98 All rationals 219.23/224.98 ->Dimension: 219.23/224.98 1 219.23/224.98 ->Bound: 219.23/224.98 2 219.23/224.98 ->Interpretation: 219.23/224.98 219.23/224.98 [0](X) = 2.X 219.23/224.98 [1](X) = 2.X + 2 219.23/224.98 [4](X) = 2.X + 1 219.23/224.98 [5](X) = 2.X + 1 219.23/224.98 [2](X) = 1/2.X 219.23/224.98 [3](X) = X 219.23/224.98 [1#](X) = X 219.23/224.98 [4#](X) = 2.X 219.23/224.98 219.23/224.98 Problem 1.2.2.1: 219.23/224.98 219.23/224.98 SCC Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Strongly Connected Components: 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 219.23/224.98 Problem 1.2.2.1: 219.23/224.98 219.23/224.98 Reduction Pair Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(1(x1:S)) 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 -> Usable rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Interpretation type: 219.23/224.98 Linear 219.23/224.98 ->Coefficients: 219.23/224.98 All rationals 219.23/224.98 ->Dimension: 219.23/224.98 1 219.23/224.98 ->Bound: 219.23/224.98 2 219.23/224.98 ->Interpretation: 219.23/224.98 219.23/224.98 [0](X) = 2.X 219.23/224.98 [1](X) = 2.X + 2 219.23/224.98 [4](X) = 2.X + 2 219.23/224.98 [5](X) = 2.X + 1/2 219.23/224.98 [2](X) = 1/2.X 219.23/224.98 [3](X) = X 219.23/224.98 [1#](X) = 1/2.X + 1/2 219.23/224.98 [4#](X) = 1/2.X + 1/2 219.23/224.98 219.23/224.98 Problem 1.2.2.1: 219.23/224.98 219.23/224.98 SCC Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 ->Strongly Connected Components: 219.23/224.98 ->->Cycle: 219.23/224.98 ->->-> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 ->->-> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 219.23/224.98 Problem 1.2.2.1: 219.23/224.98 219.23/224.98 Reduction Pair Processor: 219.23/224.98 -> Pairs: 219.23/224.98 1#(4(1(x1:S))) -> 1#(2(1(x1:S))) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.98 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.98 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.98 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.98 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.98 -> Rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.98 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.98 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.98 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.98 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.98 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.98 -> Usable rules: 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.98 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.98 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.98 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.98 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.98 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.98 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.98 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.98 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.98 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.98 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.98 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.98 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.98 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.98 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.98 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.98 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.98 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.98 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.98 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.98 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.98 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.98 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.98 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.98 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.98 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.98 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.98 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.98 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.98 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.98 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.98 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.98 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.98 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 All rationals 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = X 219.23/224.99 [1](X) = 2.X + 1 219.23/224.99 [4](X) = 2.X 219.23/224.99 [5](X) = 2.X + 1/2 219.23/224.99 [2](X) = 1/2.X 219.23/224.99 [3](X) = X 219.23/224.99 [1#](X) = 1/2.X + 1 219.23/224.99 [4#](X) = 1/2.X + 1/2 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 1#(4(x1:S)) 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 All rationals 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = 2.X 219.23/224.99 [1](X) = 2.X + 1 219.23/224.99 [4](X) = X 219.23/224.99 [5](X) = 2.X + 1/2 219.23/224.99 [2](X) = 1/2.X 219.23/224.99 [3](X) = X 219.23/224.99 [1#](X) = X 219.23/224.99 [4#](X) = 1/2.X 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 1#(2(4(3(1(x1:S))))) -> 4#(x1:S) 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 Natural Numbers 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = 0 219.23/224.99 [1](X) = 2 219.23/224.99 [4](X) = X 219.23/224.99 [5](X) = 2 219.23/224.99 [2](X) = X 219.23/224.99 [3](X) = X 219.23/224.99 [1#](X) = X + 2 219.23/224.99 [4#](X) = 2 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 1#(4(0(0(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(0(1(x1:S))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 Natural Numbers 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = 2.X 219.23/224.99 [1](X) = 2.X + 1 219.23/224.99 [4](X) = 2.X 219.23/224.99 [5](X) = 2.X + 2 219.23/224.99 [2](X) = 0 219.23/224.99 [3](X) = 2.X 219.23/224.99 [4#](X) = 2.X 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(1(0(0(x1:S)))) -> 4#(0(0(x1:S))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 Natural Numbers 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = 0 219.23/224.99 [1](X) = 2 219.23/224.99 [4](X) = 0 219.23/224.99 [5](X) = 2 219.23/224.99 [2](X) = 0 219.23/224.99 [3](X) = 0 219.23/224.99 [4#](X) = X 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(0(2(1(x1:S)))) 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 Natural Numbers 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = 0 219.23/224.99 [1](X) = 2 219.23/224.99 [4](X) = 0 219.23/224.99 [5](X) = 0 219.23/224.99 [2](X) = 0 219.23/224.99 [3](X) = 2.X 219.23/224.99 [4#](X) = 2.X 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 4#(1(0(4(x1:S)))) -> 4#(4(0(2(1(x1:S))))) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 Natural Numbers 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = X 219.23/224.99 [1](X) = 2.X + 2 219.23/224.99 [4](X) = 2.X 219.23/224.99 [5](X) = X + 2 219.23/224.99 [2](X) = 0 219.23/224.99 [3](X) = 0 219.23/224.99 [4#](X) = 2.X 219.23/224.99 219.23/224.99 Problem 1.2.2.1: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 Empty 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 There is no strongly connected component 219.23/224.99 219.23/224.99 The problem is finite. 219.23/224.99 219.23/224.99 Problem 1.2.2.2: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.99 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(2(1(x1:S))) 219.23/224.99 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.99 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.99 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.99 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.99 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 Natural Numbers 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = X 219.23/224.99 [1](X) = X 219.23/224.99 [4](X) = X 219.23/224.99 [5](X) = 2.X + 2 219.23/224.99 [2](X) = X 219.23/224.99 [3](X) = 0 219.23/224.99 [5#](X) = 2.X 219.23/224.99 219.23/224.99 Problem 1.2.2.2: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.99 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.99 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.99 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.99 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.99 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.99 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.99 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.99 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.99 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.99 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.99 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.99 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 219.23/224.99 Problem 1.2.2.2: 219.23/224.99 219.23/224.99 Reduction Pair Processor: 219.23/224.99 -> Pairs: 219.23/224.99 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.99 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.99 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.99 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.99 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.99 5#(5(0(4(x1:S)))) -> 5#(0(2(5(4(2(x1:S)))))) 219.23/224.99 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 -> Usable rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Interpretation type: 219.23/224.99 Linear 219.23/224.99 ->Coefficients: 219.23/224.99 Natural Numbers 219.23/224.99 ->Dimension: 219.23/224.99 1 219.23/224.99 ->Bound: 219.23/224.99 2 219.23/224.99 ->Interpretation: 219.23/224.99 219.23/224.99 [0](X) = 0 219.23/224.99 [1](X) = X 219.23/224.99 [4](X) = X 219.23/224.99 [5](X) = 2 219.23/224.99 [2](X) = X 219.23/224.99 [3](X) = 0 219.23/224.99 [5#](X) = 2.X 219.23/224.99 219.23/224.99 Problem 1.2.2.2: 219.23/224.99 219.23/224.99 SCC Processor: 219.23/224.99 -> Pairs: 219.23/224.99 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.99 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.99 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.99 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.99 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.99 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.99 -> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/224.99 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/224.99 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/224.99 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/224.99 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/224.99 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/224.99 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/224.99 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/224.99 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/224.99 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/224.99 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/224.99 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/224.99 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/224.99 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/224.99 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/224.99 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/224.99 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/224.99 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/224.99 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/224.99 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/224.99 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/224.99 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/224.99 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/224.99 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/224.99 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/224.99 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/224.99 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/224.99 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/224.99 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/224.99 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/224.99 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/224.99 ->Strongly Connected Components: 219.23/224.99 ->->Cycle: 219.23/224.99 ->->-> Pairs: 219.23/224.99 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/224.99 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/224.99 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/224.99 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/224.99 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/224.99 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/224.99 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/224.99 ->->-> Rules: 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/224.99 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/224.99 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/224.99 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/224.99 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/224.99 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/224.99 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/224.99 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/224.99 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(0(1(x1:S))) -> 5#(0(2(1(x1:S)))) 219.23/225.00 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = 2.X 219.23/225.00 [1](X) = X + 1 219.23/225.00 [4](X) = 2.X + 1 219.23/225.00 [5](X) = 2.X + 1/2 219.23/225.00 [2](X) = 1/2.X 219.23/225.00 [3](X) = X 219.23/225.00 [5#](X) = 1/2.X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 ->->Cycle: 219.23/225.00 ->->-> Pairs: 219.23/225.00 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 ->->-> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(1(0(0(5(x1:S))))) -> 5#(0(0(2(1(5(x1:S)))))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = 2.X 219.23/225.00 [1](X) = X + 1 219.23/225.00 [4](X) = 2.X + 1 219.23/225.00 [5](X) = X + 1 219.23/225.00 [2](X) = 1/2.X 219.23/225.00 [3](X) = X 219.23/225.00 [5#](X) = 2.X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 ->->Cycle: 219.23/225.00 ->->-> Pairs: 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 ->->-> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(4(2(5(x1:S)))) 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = X 219.23/225.00 [1](X) = X + 2 219.23/225.00 [4](X) = 2.X 219.23/225.00 [5](X) = X + 2 219.23/225.00 [2](X) = 1/2.X 219.23/225.00 [3](X) = X 219.23/225.00 [5#](X) = 1/2.X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 ->->Cycle: 219.23/225.00 ->->-> Pairs: 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 ->->-> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(1(5(x1:S)))) -> 5#(5(2(1(x1:S)))) 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = 2.X 219.23/225.00 [1](X) = X + 1/2 219.23/225.00 [4](X) = 2.X + 1/2 219.23/225.00 [5](X) = 2.X + 1/2 219.23/225.00 [2](X) = 1/2.X 219.23/225.00 [3](X) = X 219.23/225.00 [5#](X) = 1/2.X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 ->->Cycle: 219.23/225.00 ->->-> Pairs: 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 ->->-> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(1(x1:S))) -> 5#(1(3(x1:S))) 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = X 219.23/225.00 [1](X) = 2.X + 1 219.23/225.00 [4](X) = 2.X 219.23/225.00 [5](X) = 2.X + 1/2 219.23/225.00 [2](X) = 1/2.X 219.23/225.00 [3](X) = X 219.23/225.00 [5#](X) = X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 ->->Cycle: 219.23/225.00 ->->-> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 ->->-> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(4(3(1(x1:S)))) -> 5#(4(2(1(3(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = X 219.23/225.00 [1](X) = X + 1 219.23/225.00 [4](X) = 2.X 219.23/225.00 [5](X) = 1/2.X 219.23/225.00 [2](X) = 1/2.X 219.23/225.00 [3](X) = X 219.23/225.00 [5#](X) = 1/2.X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 ->->Cycle: 219.23/225.00 ->->-> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 ->->-> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 5#(2(4(1(x1:S)))) -> 5#(x1:S) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = 2.X 219.23/225.00 [1](X) = X + 1/2 219.23/225.00 [4](X) = 2.X + 1/2 219.23/225.00 [5](X) = X + 1/2 219.23/225.00 [2](X) = 1/2.X 219.23/225.00 [3](X) = X 219.23/225.00 [5#](X) = 2.X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 ->->Cycle: 219.23/225.00 ->->-> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 ->->-> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 Reduction Pair Processor: 219.23/225.00 -> Pairs: 219.23/225.00 5#(4(2(0(1(x1:S))))) -> 5#(4(0(2(1(x1:S))))) 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 -> Usable rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Interpretation type: 219.23/225.00 Linear 219.23/225.00 ->Coefficients: 219.23/225.00 All rationals 219.23/225.00 ->Dimension: 219.23/225.00 1 219.23/225.00 ->Bound: 219.23/225.00 2 219.23/225.00 ->Interpretation: 219.23/225.00 219.23/225.00 [0](X) = 1/2.X 219.23/225.00 [1](X) = 2 219.23/225.00 [4](X) = 2.X + 1 219.23/225.00 [5](X) = 1/2.X + 1/2 219.23/225.00 [2](X) = 1/2 219.23/225.00 [3](X) = 2.X 219.23/225.00 [5#](X) = X 219.23/225.00 219.23/225.00 Problem 1.2.2.2: 219.23/225.00 219.23/225.00 SCC Processor: 219.23/225.00 -> Pairs: 219.23/225.00 Empty 219.23/225.00 -> Rules: 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(0(1(x1:S))) -> 0(0(2(2(3(1(x1:S)))))) 219.23/225.00 0(0(4(5(x1:S)))) -> 0(5(0(2(4(2(x1:S)))))) 219.23/225.00 0(0(3(3(1(x1:S))))) -> 0(3(0(1(2(3(x1:S)))))) 219.23/225.00 0(1(2(0(x1:S)))) -> 2(0(2(1(0(x1:S))))) 219.23/225.00 0(4(0(4(x1:S)))) -> 0(0(3(2(4(4(x1:S)))))) 219.23/225.00 0(4(1(x1:S))) -> 0(4(2(2(1(x1:S))))) 219.23/225.00 0(4(1(x1:S))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(5(4(1(1(x1:S))))) -> 4(0(2(5(1(1(x1:S)))))) 219.23/225.00 0(2(0(1(x1:S)))) -> 0(0(2(1(3(x1:S))))) 219.23/225.00 0(2(4(3(1(x1:S))))) -> 0(2(3(1(4(2(x1:S)))))) 219.23/225.00 0(3(4(0(x1:S)))) -> 3(2(4(0(0(3(x1:S)))))) 219.23/225.00 1(0(1(4(x1:S)))) -> 2(3(1(1(4(0(x1:S)))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(2(x1:S))))) 219.23/225.00 1(0(1(x1:S))) -> 0(2(1(1(x1:S)))) 219.23/225.00 1(0(1(x1:S))) -> 1(0(3(2(1(x1:S))))) 219.23/225.00 1(0(3(1(x1:S)))) -> 4(2(3(1(1(0(x1:S)))))) 219.23/225.00 1(4(0(x1:S))) -> 1(0(3(2(4(2(x1:S)))))) 219.23/225.00 1(4(1(5(x1:S)))) -> 2(1(2(5(1(4(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(2(1(x1:S)))))) 219.23/225.00 1(4(1(x1:S))) -> 4(2(1(1(x1:S)))) 219.23/225.00 1(2(0(4(x1:S)))) -> 1(4(2(0(3(2(x1:S)))))) 219.23/225.00 1(2(4(3(1(x1:S))))) -> 1(2(3(3(1(4(x1:S)))))) 219.23/225.00 1(3(0(4(x1:S)))) -> 4(0(3(2(1(3(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(0(3(2(1(0(x1:S)))))) 219.23/225.00 4(0(0(3(1(x1:S))))) -> 4(3(2(0(0(1(x1:S)))))) 219.23/225.00 4(0(1(x1:S))) -> 4(0(2(1(x1:S)))) 219.23/225.00 4(0(5(1(x1:S)))) -> 0(2(4(2(1(5(x1:S)))))) 219.23/225.00 4(1(0(0(x1:S)))) -> 3(2(1(4(0(0(x1:S)))))) 219.23/225.00 4(1(0(4(x1:S)))) -> 4(4(0(2(1(x1:S))))) 219.23/225.00 5(0(0(1(x1:S)))) -> 0(3(2(5(1(0(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 0(2(1(5(3(x1:S))))) 219.23/225.00 5(0(1(x1:S))) -> 0(3(2(1(5(5(x1:S)))))) 219.23/225.00 5(0(1(x1:S))) -> 5(0(2(1(x1:S)))) 219.23/225.00 5(0(1(x1:S))) -> 3(0(2(3(5(1(x1:S)))))) 219.23/225.00 5(0(5(1(x1:S)))) -> 5(2(5(3(1(0(x1:S)))))) 219.23/225.00 5(0(5(x1:S))) -> 0(3(2(5(3(5(x1:S)))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(5(3(2(1(x1:S))))) 219.23/225.00 5(0(3(1(x1:S)))) -> 0(3(5(2(2(1(x1:S)))))) 219.23/225.00 5(1(0(0(5(x1:S))))) -> 5(0(0(2(1(5(x1:S)))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 4(5(5(2(1(x1:S))))) 219.23/225.00 5(4(1(5(x1:S)))) -> 2(1(5(4(2(5(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 4(5(2(1(3(3(x1:S)))))) 219.23/225.00 5(4(1(x1:S))) -> 2(4(2(5(1(3(x1:S)))))) 219.23/225.00 5(4(2(0(1(x1:S))))) -> 2(5(4(0(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(4(2(1(3(x1:S))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 5(2(4(3(2(1(x1:S)))))) 219.23/225.00 5(4(3(1(x1:S)))) -> 3(5(2(4(2(1(x1:S)))))) 219.23/225.00 5(5(0(4(x1:S)))) -> 5(0(2(5(4(2(x1:S)))))) 219.23/225.00 5(2(4(1(x1:S)))) -> 2(1(4(2(5(x1:S))))) 219.23/225.00 ->Strongly Connected Components: 219.23/225.00 There is no strongly connected component 219.23/225.00 219.23/225.00 The problem is finite. 219.23/225.01 EOF