14.76/14.89 YES 14.76/14.89 14.76/14.89 Problem 1: 14.76/14.89 14.76/14.89 (VAR v_NonEmpty:S x1:S) 14.76/14.89 (RULES 14.76/14.89 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.89 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.89 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.89 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.89 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.89 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.89 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.89 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.89 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.89 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.89 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.89 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.89 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.89 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.89 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.89 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.89 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.89 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.89 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.89 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.89 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.89 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.89 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.89 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.89 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.89 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.89 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.89 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.89 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.89 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.89 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.89 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.89 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.89 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.89 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.89 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.89 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.89 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.89 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.89 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.89 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.89 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.89 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.89 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.89 ) 14.76/14.89 14.76/14.89 Problem 1: 14.76/14.89 14.76/14.89 Dependency Pairs Processor: 14.76/14.89 -> Pairs: 14.76/14.89 0#(0(0(2(x1:S)))) -> 0#(0(3(0(2(x1:S))))) 14.76/14.89 0#(0(0(2(x1:S)))) -> 0#(3(0(2(x1:S)))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 0#(0(5(3(1(x1:S))))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 2#(0(0(5(3(1(x1:S)))))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(0(1(5(2(x1:S))))) -> 0#(1(0(3(5(2(x1:S)))))) 14.76/14.89 0#(0(1(5(2(x1:S))))) -> 0#(3(5(2(x1:S)))) 14.76/14.89 0#(0(1(5(2(x1:S))))) -> 1#(0(3(5(2(x1:S))))) 14.76/14.89 0#(0(2(2(x1:S)))) -> 0#(0(3(2(x1:S)))) 14.76/14.89 0#(0(2(2(x1:S)))) -> 0#(3(2(x1:S))) 14.76/14.89 0#(0(2(2(x1:S)))) -> 2#(3(0(0(3(2(x1:S)))))) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 0#(0(3(1(x1:S)))) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 0#(3(1(x1:S))) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 5#(4(0(0(3(1(x1:S)))))) 14.76/14.89 0#(1(1(1(2(x1:S))))) -> 0#(3(1(1(2(x1:S))))) 14.76/14.89 0#(1(1(1(2(x1:S))))) -> 1#(0(3(1(1(2(x1:S)))))) 14.76/14.89 0#(1(1(2(x1:S)))) -> 0#(3(1(1(x1:S)))) 14.76/14.89 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.76/14.89 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(1(1(2(x1:S)))) -> 2#(3(0(3(1(1(x1:S)))))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 1#(0(5(3(1(x1:S))))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 2#(1(0(5(3(1(x1:S)))))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.76/14.89 0#(1(2(2(x1:S)))) -> 0#(3(1(2(x1:S)))) 14.76/14.89 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.76/14.89 0#(1(2(2(x1:S)))) -> 2#(3(0(3(1(2(x1:S)))))) 14.76/14.89 0#(1(2(5(x1:S)))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(1(2(5(x1:S)))) -> 2#(0(5(3(1(x1:S))))) 14.76/14.89 0#(1(2(5(x1:S)))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(1(2(x1:S))) -> 0#(3(1(x1:S))) 14.76/14.89 0#(1(2(x1:S))) -> 1#(x1:S) 14.76/14.89 0#(1(2(x1:S))) -> 2#(3(0(3(1(x1:S))))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.76/14.89 0#(1(5(1(x1:S)))) -> 0#(3(5(3(1(x1:S))))) 14.76/14.89 0#(1(5(1(x1:S)))) -> 1#(0(3(5(3(1(x1:S)))))) 14.76/14.89 0#(1(5(1(x1:S)))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(3(5(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 1#(0(3(5(x1:S)))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 1#(3(0(5(2(x1:S))))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 2#(4(1(0(3(5(x1:S)))))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 2#(4(3(1(0(5(x1:S)))))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.89 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.76/14.89 0#(1(5(5(x1:S)))) -> 1#(3(0(5(5(x1:S))))) 14.76/14.89 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.76/14.89 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 2#(4(3(0(5(1(x1:S)))))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.76/14.89 0#(1(4(4(2(x1:S))))) -> 0#(4(4(4(2(x1:S))))) 14.76/14.89 0#(1(4(4(2(x1:S))))) -> 1#(0(4(4(4(2(x1:S)))))) 14.76/14.89 0#(2(1(2(x1:S)))) -> 0#(3(1(x1:S))) 14.76/14.89 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(2(1(2(x1:S)))) -> 2#(2(3(0(3(1(x1:S)))))) 14.76/14.89 0#(2(1(2(x1:S)))) -> 2#(3(0(3(1(x1:S))))) 14.76/14.89 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 0#(2(5(2(x1:S)))) -> 2#(2(3(0(5(x1:S))))) 14.76/14.89 0#(2(5(2(x1:S)))) -> 2#(3(0(5(x1:S)))) 14.76/14.89 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 1#(2(4(3(0(x1:S))))) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 2#(1(2(4(3(0(x1:S)))))) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 2#(4(3(0(x1:S)))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 0#(5(0(5(3(1(x1:S)))))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 5#(0(5(3(1(x1:S))))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 0#(0(3(1(x1:S)))) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 0#(3(1(x1:S))) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 1#(0(0(3(1(x1:S))))) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 5#(1(0(0(3(1(x1:S)))))) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 1#(4(4(1(0(5(x1:S)))))) 14.76/14.89 1#(1(4(5(x1:S)))) -> 1#(3(1(x1:S))) 14.76/14.89 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 1#(1(4(5(x1:S)))) -> 5#(4(1(3(1(x1:S))))) 14.76/14.89 1#(5(1(5(x1:S)))) -> 1#(3(5(5(3(1(x1:S)))))) 14.76/14.89 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 1#(5(1(5(x1:S)))) -> 5#(5(3(1(x1:S)))) 14.76/14.89 1#(5(1(5(x1:S)))) -> 5#(3(1(x1:S))) 14.76/14.89 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 1#(4(0(1(5(x1:S))))) -> 1#(3(0(5(x1:S)))) 14.76/14.89 1#(4(0(1(5(x1:S))))) -> 1#(4(1(3(0(5(x1:S)))))) 14.76/14.89 2#(0(1(2(x1:S)))) -> 0#(3(1(x1:S))) 14.76/14.89 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 2#(0(1(2(x1:S)))) -> 2#(2(3(0(3(1(x1:S)))))) 14.76/14.89 2#(0(1(2(x1:S)))) -> 2#(3(0(3(1(x1:S))))) 14.76/14.89 2#(0(1(5(2(x1:S))))) -> 0#(3(5(2(x1:S)))) 14.76/14.89 2#(0(1(5(2(x1:S))))) -> 1#(0(3(5(2(x1:S))))) 14.76/14.89 2#(0(1(5(2(x1:S))))) -> 2#(1(0(3(5(2(x1:S)))))) 14.76/14.89 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 2#(0(1(5(x1:S)))) -> 1#(3(0(5(x1:S)))) 14.76/14.89 2#(0(1(5(x1:S)))) -> 2#(1(3(0(5(x1:S))))) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 0#(3(1(5(2(2(x1:S)))))) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 1#(4(2(3(0(x1:S))))) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 2#(1(4(2(3(0(x1:S)))))) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 2#(3(0(x1:S))) 14.76/14.89 2#(2(1(1(2(x1:S))))) -> 1#(3(1(2(x1:S)))) 14.76/14.89 2#(2(1(1(2(x1:S))))) -> 2#(1(3(1(2(x1:S))))) 14.76/14.89 2#(2(1(1(2(x1:S))))) -> 2#(2(1(3(1(2(x1:S)))))) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 2#(4(1(5(5(2(x1:S)))))) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 0#(5(3(1(2(x1:S))))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 5#(0(1(2(x1:S)))) -> 2#(3(0(5(1(x1:S))))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.76/14.89 5#(0(1(2(x1:S)))) -> 5#(3(1(2(x1:S)))) 14.76/14.89 5#(0(1(4(5(x1:S))))) -> 0#(3(5(5(x1:S)))) 14.76/14.89 5#(0(1(4(5(x1:S))))) -> 1#(0(3(5(5(x1:S))))) 14.76/14.89 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.76/14.89 5#(5(1(4(5(x1:S))))) -> 1#(3(5(5(x1:S)))) 14.76/14.89 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.89 5#(5(1(4(5(x1:S))))) -> 5#(4(1(3(5(5(x1:S)))))) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 1#(3(5(2(0(x1:S))))) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.76/14.89 -> Rules: 14.76/14.89 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.89 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.89 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.89 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.89 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.89 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.89 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.89 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.89 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.89 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.89 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.89 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.89 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.89 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.89 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.89 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.89 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.89 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.89 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.89 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.89 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.89 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.89 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.89 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.89 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.89 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.89 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.89 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.89 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.89 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.89 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.89 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.89 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.89 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.89 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.89 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.89 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.89 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.89 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.89 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.89 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.89 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.89 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.89 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.89 14.76/14.89 Problem 1: 14.76/14.89 14.76/14.89 SCC Processor: 14.76/14.89 -> Pairs: 14.76/14.89 0#(0(0(2(x1:S)))) -> 0#(0(3(0(2(x1:S))))) 14.76/14.89 0#(0(0(2(x1:S)))) -> 0#(3(0(2(x1:S)))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 0#(0(5(3(1(x1:S))))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 2#(0(0(5(3(1(x1:S)))))) 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(0(1(5(2(x1:S))))) -> 0#(1(0(3(5(2(x1:S)))))) 14.76/14.89 0#(0(1(5(2(x1:S))))) -> 0#(3(5(2(x1:S)))) 14.76/14.89 0#(0(1(5(2(x1:S))))) -> 1#(0(3(5(2(x1:S))))) 14.76/14.89 0#(0(2(2(x1:S)))) -> 0#(0(3(2(x1:S)))) 14.76/14.89 0#(0(2(2(x1:S)))) -> 0#(3(2(x1:S))) 14.76/14.89 0#(0(2(2(x1:S)))) -> 2#(3(0(0(3(2(x1:S)))))) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 0#(0(3(1(x1:S)))) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 0#(3(1(x1:S))) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 5#(4(0(0(3(1(x1:S)))))) 14.76/14.89 0#(1(1(1(2(x1:S))))) -> 0#(3(1(1(2(x1:S))))) 14.76/14.89 0#(1(1(1(2(x1:S))))) -> 1#(0(3(1(1(2(x1:S)))))) 14.76/14.89 0#(1(1(2(x1:S)))) -> 0#(3(1(1(x1:S)))) 14.76/14.89 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.76/14.89 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(1(1(2(x1:S)))) -> 2#(3(0(3(1(1(x1:S)))))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 1#(0(5(3(1(x1:S))))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 2#(1(0(5(3(1(x1:S)))))) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.76/14.89 0#(1(2(2(x1:S)))) -> 0#(3(1(2(x1:S)))) 14.76/14.89 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.76/14.89 0#(1(2(2(x1:S)))) -> 2#(3(0(3(1(2(x1:S)))))) 14.76/14.89 0#(1(2(5(x1:S)))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(1(2(5(x1:S)))) -> 2#(0(5(3(1(x1:S))))) 14.76/14.89 0#(1(2(5(x1:S)))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(1(2(x1:S))) -> 0#(3(1(x1:S))) 14.76/14.89 0#(1(2(x1:S))) -> 1#(x1:S) 14.76/14.89 0#(1(2(x1:S))) -> 2#(3(0(3(1(x1:S))))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.76/14.89 0#(1(5(1(x1:S)))) -> 0#(3(5(3(1(x1:S))))) 14.76/14.89 0#(1(5(1(x1:S)))) -> 1#(0(3(5(3(1(x1:S)))))) 14.76/14.89 0#(1(5(1(x1:S)))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(3(5(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 1#(0(3(5(x1:S)))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 1#(3(0(5(2(x1:S))))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 2#(4(1(0(3(5(x1:S)))))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 2#(4(3(1(0(5(x1:S)))))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.89 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.76/14.89 0#(1(5(5(x1:S)))) -> 1#(3(0(5(5(x1:S))))) 14.76/14.89 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.76/14.89 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 2#(4(3(0(5(1(x1:S)))))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.76/14.89 0#(1(4(4(2(x1:S))))) -> 0#(4(4(4(2(x1:S))))) 14.76/14.89 0#(1(4(4(2(x1:S))))) -> 1#(0(4(4(4(2(x1:S)))))) 14.76/14.89 0#(2(1(2(x1:S)))) -> 0#(3(1(x1:S))) 14.76/14.89 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(2(1(2(x1:S)))) -> 2#(2(3(0(3(1(x1:S)))))) 14.76/14.89 0#(2(1(2(x1:S)))) -> 2#(3(0(3(1(x1:S))))) 14.76/14.89 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 0#(2(5(2(x1:S)))) -> 2#(2(3(0(5(x1:S))))) 14.76/14.89 0#(2(5(2(x1:S)))) -> 2#(3(0(5(x1:S)))) 14.76/14.89 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 1#(2(4(3(0(x1:S))))) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 2#(1(2(4(3(0(x1:S)))))) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 2#(4(3(0(x1:S)))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 0#(5(0(5(3(1(x1:S)))))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 0#(5(3(1(x1:S)))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 5#(0(5(3(1(x1:S))))) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 5#(3(1(x1:S))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 0#(0(3(1(x1:S)))) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 0#(3(1(x1:S))) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 1#(0(0(3(1(x1:S))))) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 5#(1(0(0(3(1(x1:S)))))) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 1#(4(4(1(0(5(x1:S)))))) 14.76/14.89 1#(1(4(5(x1:S)))) -> 1#(3(1(x1:S))) 14.76/14.89 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 1#(1(4(5(x1:S)))) -> 5#(4(1(3(1(x1:S))))) 14.76/14.89 1#(5(1(5(x1:S)))) -> 1#(3(5(5(3(1(x1:S)))))) 14.76/14.89 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 1#(5(1(5(x1:S)))) -> 5#(5(3(1(x1:S)))) 14.76/14.89 1#(5(1(5(x1:S)))) -> 5#(3(1(x1:S))) 14.76/14.89 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 1#(4(0(1(5(x1:S))))) -> 1#(3(0(5(x1:S)))) 14.76/14.89 1#(4(0(1(5(x1:S))))) -> 1#(4(1(3(0(5(x1:S)))))) 14.76/14.89 2#(0(1(2(x1:S)))) -> 0#(3(1(x1:S))) 14.76/14.89 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 2#(0(1(2(x1:S)))) -> 2#(2(3(0(3(1(x1:S)))))) 14.76/14.89 2#(0(1(2(x1:S)))) -> 2#(3(0(3(1(x1:S))))) 14.76/14.89 2#(0(1(5(2(x1:S))))) -> 0#(3(5(2(x1:S)))) 14.76/14.89 2#(0(1(5(2(x1:S))))) -> 1#(0(3(5(2(x1:S))))) 14.76/14.89 2#(0(1(5(2(x1:S))))) -> 2#(1(0(3(5(2(x1:S)))))) 14.76/14.89 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 2#(0(1(5(x1:S)))) -> 1#(3(0(5(x1:S)))) 14.76/14.89 2#(0(1(5(x1:S)))) -> 2#(1(3(0(5(x1:S))))) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 0#(3(1(5(2(2(x1:S)))))) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 1#(4(2(3(0(x1:S))))) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 2#(1(4(2(3(0(x1:S)))))) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 2#(3(0(x1:S))) 14.76/14.89 2#(2(1(1(2(x1:S))))) -> 1#(3(1(2(x1:S)))) 14.76/14.89 2#(2(1(1(2(x1:S))))) -> 2#(1(3(1(2(x1:S))))) 14.76/14.89 2#(2(1(1(2(x1:S))))) -> 2#(2(1(3(1(2(x1:S)))))) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 2#(4(1(5(5(2(x1:S)))))) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 0#(5(3(1(2(x1:S))))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 5#(0(1(2(x1:S)))) -> 2#(3(0(5(1(x1:S))))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.76/14.89 5#(0(1(2(x1:S)))) -> 5#(3(1(2(x1:S)))) 14.76/14.89 5#(0(1(4(5(x1:S))))) -> 0#(3(5(5(x1:S)))) 14.76/14.89 5#(0(1(4(5(x1:S))))) -> 1#(0(3(5(5(x1:S))))) 14.76/14.89 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.76/14.89 5#(5(1(4(5(x1:S))))) -> 1#(3(5(5(x1:S)))) 14.76/14.89 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.89 5#(5(1(4(5(x1:S))))) -> 5#(4(1(3(5(5(x1:S)))))) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 1#(3(5(2(0(x1:S))))) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.76/14.89 -> Rules: 14.76/14.89 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.89 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.89 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.89 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.89 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.89 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.89 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.89 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.89 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.89 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.89 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.89 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.89 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.89 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.89 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.89 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.89 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.89 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.89 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.89 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.89 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.89 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.89 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.89 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.89 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.89 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.89 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.89 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.89 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.89 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.89 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.89 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.89 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.89 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.89 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.89 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.89 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.89 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.89 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.89 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.89 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.89 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.89 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.89 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.89 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.89 ->Strongly Connected Components: 14.76/14.89 ->->Cycle: 14.76/14.89 ->->-> Pairs: 14.76/14.89 0#(0(1(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(0(4(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.76/14.89 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.76/14.89 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.76/14.89 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(1(2(x1:S))) -> 1#(x1:S) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.76/14.89 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.76/14.89 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.89 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.76/14.89 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.76/14.89 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.76/14.89 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.89 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.76/14.89 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.89 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.89 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.76/14.89 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.76/14.89 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.76/14.89 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.76/14.89 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.76/14.89 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.89 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.76/14.89 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.76/14.89 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.76/14.89 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.89 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.76/14.89 ->->-> Rules: 14.76/14.89 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.89 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.89 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.89 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.89 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.89 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.89 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.89 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.89 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.89 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.89 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.89 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.89 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.90 14.76/14.90 Problem 1: 14.76/14.90 14.76/14.90 Reduction Pair Processor: 14.76/14.90 -> Pairs: 14.76/14.90 0#(0(1(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(0(4(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.76/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.76/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.76/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.76/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.76/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.76/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.76/14.90 -> Rules: 14.76/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.90 -> Usable rules: 14.76/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.90 ->Interpretation type: 14.76/14.90 Linear 14.76/14.90 ->Coefficients: 14.76/14.90 Natural Numbers 14.76/14.90 ->Dimension: 14.76/14.90 1 14.76/14.90 ->Bound: 14.76/14.90 2 14.76/14.90 ->Interpretation: 14.76/14.90 14.76/14.90 [0](X) = 2.X + 2 14.76/14.90 [1](X) = X 14.76/14.90 [2](X) = 2.X + 2 14.76/14.90 [5](X) = 2.X + 2 14.76/14.90 [3](X) = X 14.76/14.90 [4](X) = X 14.76/14.90 [0#](X) = 2.X + 2 14.76/14.90 [1#](X) = X 14.76/14.90 [2#](X) = 2.X + 2 14.76/14.90 [5#](X) = 2.X + 2 14.76/14.90 14.76/14.90 Problem 1: 14.76/14.90 14.76/14.90 SCC Processor: 14.76/14.90 -> Pairs: 14.76/14.90 0#(1(0(4(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.76/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.76/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.76/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.76/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.76/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.76/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.76/14.90 -> Rules: 14.76/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.90 ->Strongly Connected Components: 14.76/14.90 ->->Cycle: 14.76/14.90 ->->-> Pairs: 14.76/14.90 0#(1(0(4(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.76/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.76/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.76/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.76/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.76/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.76/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.76/14.90 ->->-> Rules: 14.76/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.90 14.76/14.90 Problem 1: 14.76/14.90 14.76/14.90 Reduction Pair Processor: 14.76/14.90 -> Pairs: 14.76/14.90 0#(1(0(4(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.76/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.76/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.76/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.76/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.76/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.76/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.76/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.76/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.76/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.76/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.76/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.76/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.76/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.76/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.76/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.76/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.76/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.76/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.76/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.76/14.90 -> Rules: 14.76/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.90 -> Usable rules: 14.76/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.76/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.76/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.76/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.76/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.76/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.76/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.76/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.76/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.76/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.76/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.76/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.76/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.76/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.76/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.76/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.76/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.76/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.76/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.76/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.76/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.76/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.76/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.76/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.76/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.76/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.76/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.76/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.76/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.76/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.76/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.76/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.76/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.76/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.76/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.76/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.76/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.76/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.76/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.76/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.76/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.76/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.76/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.76/14.90 ->Interpretation type: 14.76/14.90 Linear 14.76/14.90 ->Coefficients: 14.76/14.90 Natural Numbers 14.76/14.90 ->Dimension: 14.76/14.90 1 14.76/14.90 ->Bound: 14.76/14.90 2 14.76/14.90 ->Interpretation: 14.76/14.90 14.76/14.90 [0](X) = 2.X + 2 14.76/14.90 [1](X) = 2.X + 2 14.76/14.90 [2](X) = 2.X + 2 14.85/14.90 [5](X) = X 14.85/14.90 [3](X) = X 14.85/14.90 [4](X) = X 14.85/14.90 [0#](X) = 2.X + 2 14.85/14.90 [1#](X) = 2.X + 2 14.85/14.90 [2#](X) = 2.X + 2 14.85/14.90 [5#](X) = X 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 SCC Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 -> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 ->Strongly Connected Components: 14.85/14.90 ->->Cycle: 14.85/14.90 ->->-> Pairs: 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 ->->-> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 Reduction Pair Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(1(x1:S)) 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 -> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 -> Usable rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 ->Interpretation type: 14.85/14.90 Linear 14.85/14.90 ->Coefficients: 14.85/14.90 Natural Numbers 14.85/14.90 ->Dimension: 14.85/14.90 1 14.85/14.90 ->Bound: 14.85/14.90 2 14.85/14.90 ->Interpretation: 14.85/14.90 14.85/14.90 [0](X) = 2.X + 2 14.85/14.90 [1](X) = 2.X + 2 14.85/14.90 [2](X) = 2.X + 2 14.85/14.90 [5](X) = X 14.85/14.90 [3](X) = X 14.85/14.90 [4](X) = X 14.85/14.90 [0#](X) = 2.X + 2 14.85/14.90 [1#](X) = 2.X + 2 14.85/14.90 [2#](X) = X + 1 14.85/14.90 [5#](X) = X 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 SCC Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 -> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 ->Strongly Connected Components: 14.85/14.90 ->->Cycle: 14.85/14.90 ->->-> Pairs: 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 ->->-> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 Reduction Pair Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 -> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 -> Usable rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 ->Interpretation type: 14.85/14.90 Linear 14.85/14.90 ->Coefficients: 14.85/14.90 Natural Numbers 14.85/14.90 ->Dimension: 14.85/14.90 1 14.85/14.90 ->Bound: 14.85/14.90 2 14.85/14.90 ->Interpretation: 14.85/14.90 14.85/14.90 [0](X) = 2.X + 1 14.85/14.90 [1](X) = X 14.85/14.90 [2](X) = 2.X + 1 14.85/14.90 [5](X) = 2.X + 1 14.85/14.90 [3](X) = X 14.85/14.90 [4](X) = X 14.85/14.90 [0#](X) = 2.X + 2 14.85/14.90 [1#](X) = X + 1 14.85/14.90 [2#](X) = 2.X + 1 14.85/14.90 [5#](X) = 2.X + 2 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 SCC Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 -> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 ->Strongly Connected Components: 14.85/14.90 ->->Cycle: 14.85/14.90 ->->-> Pairs: 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 ->->-> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 Reduction Pair Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(2(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 -> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 -> Usable rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 ->Interpretation type: 14.85/14.90 Linear 14.85/14.90 ->Coefficients: 14.85/14.90 Natural Numbers 14.85/14.90 ->Dimension: 14.85/14.90 1 14.85/14.90 ->Bound: 14.85/14.90 2 14.85/14.90 ->Interpretation: 14.85/14.90 14.85/14.90 [0](X) = 2.X + 2 14.85/14.90 [1](X) = 2.X + 2 14.85/14.90 [2](X) = 2.X + 2 14.85/14.90 [5](X) = 2.X + 2 14.85/14.90 [3](X) = X 14.85/14.90 [4](X) = X 14.85/14.90 [0#](X) = 2.X 14.85/14.90 [1#](X) = 2.X 14.85/14.90 [2#](X) = 2.X + 2 14.85/14.90 [5#](X) = 2.X 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 SCC Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 -> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 ->Strongly Connected Components: 14.85/14.90 ->->Cycle: 14.85/14.90 ->->-> Pairs: 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.90 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.90 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.90 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.90 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.90 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.90 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.90 ->->-> Rules: 14.85/14.90 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.90 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.90 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.90 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.90 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.90 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.90 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.90 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.90 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.90 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.90 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.90 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.90 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.90 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.90 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.90 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.90 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.90 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.90 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.90 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.90 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.90 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.90 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.90 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.90 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.90 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.90 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.90 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.90 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.90 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.90 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.90 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.90 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.90 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.90 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.90 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.90 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.90 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.90 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.90 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.90 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.90 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.90 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.90 14.85/14.90 Problem 1: 14.85/14.90 14.85/14.90 Reduction Pair Processor: 14.85/14.90 -> Pairs: 14.85/14.90 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.90 0#(1(2(2(x1:S)))) -> 1#(2(x1:S)) 14.85/14.90 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.90 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.90 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.90 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.90 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.90 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.90 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.90 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.90 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.90 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.90 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.90 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 -> Usable rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Interpretation type: 14.85/14.91 Linear 14.85/14.91 ->Coefficients: 14.85/14.91 Natural Numbers 14.85/14.91 ->Dimension: 14.85/14.91 1 14.85/14.91 ->Bound: 14.85/14.91 2 14.85/14.91 ->Interpretation: 14.85/14.91 14.85/14.91 [0](X) = 2.X + 2 14.85/14.91 [1](X) = 2.X + 2 14.85/14.91 [2](X) = 2.X + 2 14.85/14.91 [5](X) = 2.X + 2 14.85/14.91 [3](X) = X 14.85/14.91 [4](X) = X 14.85/14.91 [0#](X) = 2.X + 2 14.85/14.91 [1#](X) = X + 2 14.85/14.91 [2#](X) = X + 2 14.85/14.91 [5#](X) = 2.X + 2 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 SCC Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.91 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Strongly Connected Components: 14.85/14.91 ->->Cycle: 14.85/14.91 ->->-> Pairs: 14.85/14.91 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.91 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 ->->-> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 Reduction Pair Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.91 0#(1(2(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 -> Usable rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Interpretation type: 14.85/14.91 Linear 14.85/14.91 ->Coefficients: 14.85/14.91 Natural Numbers 14.85/14.91 ->Dimension: 14.85/14.91 1 14.85/14.91 ->Bound: 14.85/14.91 2 14.85/14.91 ->Interpretation: 14.85/14.91 14.85/14.91 [0](X) = 2.X + 2 14.85/14.91 [1](X) = X 14.85/14.91 [2](X) = 2.X + 2 14.85/14.91 [5](X) = X 14.85/14.91 [3](X) = X 14.85/14.91 [4](X) = X 14.85/14.91 [0#](X) = 2.X + 2 14.85/14.91 [1#](X) = X 14.85/14.91 [2#](X) = 2.X 14.85/14.91 [5#](X) = X 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 SCC Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.91 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Strongly Connected Components: 14.85/14.91 ->->Cycle: 14.85/14.91 ->->-> Pairs: 14.85/14.91 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.91 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 ->->-> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 Reduction Pair Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.91 0#(1(2(x1:S))) -> 1#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 -> Usable rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Interpretation type: 14.85/14.91 Linear 14.85/14.91 ->Coefficients: 14.85/14.91 Natural Numbers 14.85/14.91 ->Dimension: 14.85/14.91 1 14.85/14.91 ->Bound: 14.85/14.91 2 14.85/14.91 ->Interpretation: 14.85/14.91 14.85/14.91 [0](X) = X 14.85/14.91 [1](X) = 2.X + 2 14.85/14.91 [2](X) = 2.X + 2 14.85/14.91 [5](X) = 2.X + 2 14.85/14.91 [3](X) = X 14.85/14.91 [4](X) = X 14.85/14.91 [0#](X) = 2.X 14.85/14.91 [1#](X) = 2.X 14.85/14.91 [2#](X) = 2.X + 2 14.85/14.91 [5#](X) = 2.X 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 SCC Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(2(1(x1:S)))) -> 0#(1(2(4(1(3(x1:S)))))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Strongly Connected Components: 14.85/14.91 ->->Cycle: 14.85/14.91 ->->-> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 ->->-> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 Reduction Pair Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(5(0(x1:S))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 -> Usable rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Interpretation type: 14.85/14.91 Linear 14.85/14.91 ->Coefficients: 14.85/14.91 Natural Numbers 14.85/14.91 ->Dimension: 14.85/14.91 1 14.85/14.91 ->Bound: 14.85/14.91 2 14.85/14.91 ->Interpretation: 14.85/14.91 14.85/14.91 [0](X) = 2.X + 2 14.85/14.91 [1](X) = 2.X + 2 14.85/14.91 [2](X) = 2.X + 2 14.85/14.91 [5](X) = 2.X + 2 14.85/14.91 [3](X) = X 14.85/14.91 [4](X) = X 14.85/14.91 [0#](X) = 2.X + 2 14.85/14.91 [1#](X) = 2.X 14.85/14.91 [2#](X) = 2.X + 1 14.85/14.91 [5#](X) = 2.X + 1 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 SCC Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Strongly Connected Components: 14.85/14.91 ->->Cycle: 14.85/14.91 ->->-> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 ->->-> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 Reduction Pair Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 -> Usable rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Interpretation type: 14.85/14.91 Linear 14.85/14.91 ->Coefficients: 14.85/14.91 Natural Numbers 14.85/14.91 ->Dimension: 14.85/14.91 1 14.85/14.91 ->Bound: 14.85/14.91 2 14.85/14.91 ->Interpretation: 14.85/14.91 14.85/14.91 [0](X) = 2.X + 2 14.85/14.91 [1](X) = 2.X + 2 14.85/14.91 [2](X) = 2.X + 2 14.85/14.91 [5](X) = 2.X + 2 14.85/14.91 [3](X) = X 14.85/14.91 [4](X) = X 14.85/14.91 [0#](X) = 2.X + 2 14.85/14.91 [1#](X) = 2.X + 2 14.85/14.91 [2#](X) = 2.X + 2 14.85/14.91 [5#](X) = 2.X + 2 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 SCC Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Strongly Connected Components: 14.85/14.91 ->->Cycle: 14.85/14.91 ->->-> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 ->->-> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 Reduction Pair Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 1#(0(5(0(x1:S)))) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.91 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.91 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.91 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.91 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.91 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.91 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.91 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.91 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.91 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.91 -> Rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 -> Usable rules: 14.85/14.91 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.91 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.91 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.91 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.91 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.91 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.91 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.91 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.91 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.91 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.91 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.91 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.91 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.91 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.91 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.91 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.91 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.91 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.91 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.91 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.91 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.91 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.91 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.91 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.91 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.91 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.91 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.91 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.91 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.91 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.91 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.91 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.91 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.91 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.91 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.91 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.91 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.91 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.91 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.91 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.91 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.91 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.91 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.91 ->Interpretation type: 14.85/14.91 Linear 14.85/14.91 ->Coefficients: 14.85/14.91 Natural Numbers 14.85/14.91 ->Dimension: 14.85/14.91 1 14.85/14.91 ->Bound: 14.85/14.91 2 14.85/14.91 ->Interpretation: 14.85/14.91 14.85/14.91 [0](X) = X 14.85/14.91 [1](X) = 2.X + 2 14.85/14.91 [2](X) = 2.X + 2 14.85/14.91 [5](X) = 2.X + 2 14.85/14.91 [3](X) = X 14.85/14.91 [4](X) = X 14.85/14.91 [0#](X) = 2.X + 2 14.85/14.91 [1#](X) = X + 1 14.85/14.91 [2#](X) = X + 1 14.85/14.91 [5#](X) = 2.X + 2 14.85/14.91 14.85/14.91 Problem 1: 14.85/14.91 14.85/14.91 SCC Processor: 14.85/14.91 -> Pairs: 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.91 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.91 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.91 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.91 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.91 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.91 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.91 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.91 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.91 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Strongly Connected Components: 14.85/14.92 ->->Cycle: 14.85/14.92 ->->-> Pairs: 14.85/14.92 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.92 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 ->->-> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 Reduction Pair Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(0(5(x1:S))))) -> 5#(0(x1:S)) 14.85/14.92 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 -> Usable rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Interpretation type: 14.85/14.92 Linear 14.85/14.92 ->Coefficients: 14.85/14.92 Natural Numbers 14.85/14.92 ->Dimension: 14.85/14.92 1 14.85/14.92 ->Bound: 14.85/14.92 2 14.85/14.92 ->Interpretation: 14.85/14.92 14.85/14.92 [0](X) = 2.X + 2 14.85/14.92 [1](X) = 2.X + 2 14.85/14.92 [2](X) = 2.X + 2 14.85/14.92 [5](X) = 2.X + 2 14.85/14.92 [3](X) = X 14.85/14.92 [4](X) = X 14.85/14.92 [0#](X) = 2.X + 2 14.85/14.92 [1#](X) = X + 2 14.85/14.92 [2#](X) = 2.X + 2 14.85/14.92 [5#](X) = 2.X + 2 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 SCC Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Strongly Connected Components: 14.85/14.92 ->->Cycle: 14.85/14.92 ->->-> Pairs: 14.85/14.92 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 ->->-> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 Reduction Pair Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(0(5(x1:S))))) -> 5#(1(0(5(0(x1:S))))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 -> Usable rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Interpretation type: 14.85/14.92 Linear 14.85/14.92 ->Coefficients: 14.85/14.92 Natural Numbers 14.85/14.92 ->Dimension: 14.85/14.92 1 14.85/14.92 ->Bound: 14.85/14.92 2 14.85/14.92 ->Interpretation: 14.85/14.92 14.85/14.92 [0](X) = 2.X + 2 14.85/14.92 [1](X) = 2.X + 2 14.85/14.92 [2](X) = 2.X + 2 14.85/14.92 [5](X) = 2.X + 2 14.85/14.92 [3](X) = X 14.85/14.92 [4](X) = X 14.85/14.92 [0#](X) = 2.X + 1 14.85/14.92 [1#](X) = 2.X 14.85/14.92 [2#](X) = 2.X + 2 14.85/14.92 [5#](X) = 2.X 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 SCC Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Strongly Connected Components: 14.85/14.92 ->->Cycle: 14.85/14.92 ->->-> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 ->->-> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 Reduction Pair Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(2(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 -> Usable rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Interpretation type: 14.85/14.92 Linear 14.85/14.92 ->Coefficients: 14.85/14.92 Natural Numbers 14.85/14.92 ->Dimension: 14.85/14.92 1 14.85/14.92 ->Bound: 14.85/14.92 2 14.85/14.92 ->Interpretation: 14.85/14.92 14.85/14.92 [0](X) = 2.X + 2 14.85/14.92 [1](X) = 2.X + 2 14.85/14.92 [2](X) = 2.X + 2 14.85/14.92 [5](X) = 2.X + 2 14.85/14.92 [3](X) = X 14.85/14.92 [4](X) = X 14.85/14.92 [0#](X) = X + 2 14.85/14.92 [1#](X) = 2.X + 2 14.85/14.92 [2#](X) = 2.X 14.85/14.92 [5#](X) = 2.X + 2 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 SCC Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Strongly Connected Components: 14.85/14.92 ->->Cycle: 14.85/14.92 ->->-> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 ->->-> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 Reduction Pair Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 -> Usable rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Interpretation type: 14.85/14.92 Linear 14.85/14.92 ->Coefficients: 14.85/14.92 Natural Numbers 14.85/14.92 ->Dimension: 14.85/14.92 1 14.85/14.92 ->Bound: 14.85/14.92 2 14.85/14.92 ->Interpretation: 14.85/14.92 14.85/14.92 [0](X) = 2.X + 2 14.85/14.92 [1](X) = 2.X + 2 14.85/14.92 [2](X) = X 14.85/14.92 [5](X) = 2.X + 2 14.85/14.92 [3](X) = X 14.85/14.92 [4](X) = X 14.85/14.92 [0#](X) = 2.X + 2 14.85/14.92 [1#](X) = 2.X + 2 14.85/14.92 [2#](X) = 2.X + 2 14.85/14.92 [5#](X) = 2.X + 2 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 SCC Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Strongly Connected Components: 14.85/14.92 ->->Cycle: 14.85/14.92 ->->-> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 ->->-> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 Reduction Pair Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 1#(0(5(x1:S))) 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 -> Usable rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Interpretation type: 14.85/14.92 Linear 14.85/14.92 ->Coefficients: 14.85/14.92 Natural Numbers 14.85/14.92 ->Dimension: 14.85/14.92 1 14.85/14.92 ->Bound: 14.85/14.92 2 14.85/14.92 ->Interpretation: 14.85/14.92 14.85/14.92 [0](X) = 2.X + 2 14.85/14.92 [1](X) = 2.X + 2 14.85/14.92 [2](X) = 2.X + 2 14.85/14.92 [5](X) = 2.X + 2 14.85/14.92 [3](X) = X 14.85/14.92 [4](X) = X 14.85/14.92 [0#](X) = 2.X + 2 14.85/14.92 [1#](X) = 2.X + 1 14.85/14.92 [2#](X) = X + 2 14.85/14.92 [5#](X) = 2.X + 2 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 SCC Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 ->Strongly Connected Components: 14.85/14.92 ->->Cycle: 14.85/14.92 ->->-> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 ->->-> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.92 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.92 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.92 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.92 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.92 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.92 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.92 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.92 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.92 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.92 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.92 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.92 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.92 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.92 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.92 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.92 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.92 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.92 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.92 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.92 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.92 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.92 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.92 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.92 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.92 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.92 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.92 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.92 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.92 14.85/14.92 Problem 1: 14.85/14.92 14.85/14.92 Reduction Pair Processor: 14.85/14.92 -> Pairs: 14.85/14.92 0#(1(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.92 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.92 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.92 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.92 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.92 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.92 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.92 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.92 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.92 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.92 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.92 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.92 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.92 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.92 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.92 -> Rules: 14.85/14.92 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.92 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.92 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.92 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.92 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.92 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.92 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.92 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.92 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.92 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.92 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.92 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.92 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.92 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.92 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 -> Usable rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Interpretation type: 14.85/14.93 Linear 14.85/14.93 ->Coefficients: 14.85/14.93 Natural Numbers 14.85/14.93 ->Dimension: 14.85/14.93 1 14.85/14.93 ->Bound: 14.85/14.93 2 14.85/14.93 ->Interpretation: 14.85/14.93 14.85/14.93 [0](X) = 2.X + 2 14.85/14.93 [1](X) = 2.X + 2 14.85/14.93 [2](X) = 2.X + 2 14.85/14.93 [5](X) = 2.X + 2 14.85/14.93 [3](X) = X 14.85/14.93 [4](X) = X 14.85/14.93 [0#](X) = 2.X + 1 14.85/14.93 [1#](X) = 2.X 14.85/14.93 [2#](X) = X + 2 14.85/14.93 [5#](X) = 2.X + 2 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 SCC Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Strongly Connected Components: 14.85/14.93 ->->Cycle: 14.85/14.93 ->->-> Pairs: 14.85/14.93 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 ->->-> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 Reduction Pair Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(5(5(x1:S)))) -> 0#(5(5(x1:S))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 -> Usable rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Interpretation type: 14.85/14.93 Linear 14.85/14.93 ->Coefficients: 14.85/14.93 Natural Numbers 14.85/14.93 ->Dimension: 14.85/14.93 1 14.85/14.93 ->Bound: 14.85/14.93 2 14.85/14.93 ->Interpretation: 14.85/14.93 14.85/14.93 [0](X) = 2.X + 2 14.85/14.93 [1](X) = 2.X + 2 14.85/14.93 [2](X) = 2.X + 2 14.85/14.93 [5](X) = 2.X + 2 14.85/14.93 [3](X) = X 14.85/14.93 [4](X) = X 14.85/14.93 [0#](X) = 2.X + 2 14.85/14.93 [1#](X) = 2.X + 2 14.85/14.93 [2#](X) = X + 1 14.85/14.93 [5#](X) = 2.X + 2 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 SCC Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Strongly Connected Components: 14.85/14.93 ->->Cycle: 14.85/14.93 ->->-> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 ->->-> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 Reduction Pair Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 1#(5(2(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 -> Usable rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Interpretation type: 14.85/14.93 Linear 14.85/14.93 ->Coefficients: 14.85/14.93 Natural Numbers 14.85/14.93 ->Dimension: 14.85/14.93 1 14.85/14.93 ->Bound: 14.85/14.93 2 14.85/14.93 ->Interpretation: 14.85/14.93 14.85/14.93 [0](X) = 2.X + 2 14.85/14.93 [1](X) = X 14.85/14.93 [2](X) = 2.X + 2 14.85/14.93 [5](X) = 2.X + 2 14.85/14.93 [3](X) = X 14.85/14.93 [4](X) = X 14.85/14.93 [0#](X) = 2.X + 2 14.85/14.93 [1#](X) = X 14.85/14.93 [2#](X) = 2.X + 1 14.85/14.93 [5#](X) = 2.X + 2 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 SCC Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Strongly Connected Components: 14.85/14.93 ->->Cycle: 14.85/14.93 ->->-> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 ->->-> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 Reduction Pair Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 0#(5(1(x1:S))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 -> Usable rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Interpretation type: 14.85/14.93 Linear 14.85/14.93 ->Coefficients: 14.85/14.93 Natural Numbers 14.85/14.93 ->Dimension: 14.85/14.93 1 14.85/14.93 ->Bound: 14.85/14.93 2 14.85/14.93 ->Interpretation: 14.85/14.93 14.85/14.93 [0](X) = 2.X + 2 14.85/14.93 [1](X) = 2.X + 2 14.85/14.93 [2](X) = 2.X + 2 14.85/14.93 [5](X) = 2.X + 2 14.85/14.93 [3](X) = X 14.85/14.93 [4](X) = X 14.85/14.93 [0#](X) = 2.X + 2 14.85/14.93 [1#](X) = 2.X + 1 14.85/14.93 [2#](X) = X + 1 14.85/14.93 [5#](X) = 2.X + 1 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 SCC Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Strongly Connected Components: 14.85/14.93 ->->Cycle: 14.85/14.93 ->->-> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 ->->-> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 Reduction Pair Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 -> Usable rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Interpretation type: 14.85/14.93 Linear 14.85/14.93 ->Coefficients: 14.85/14.93 Natural Numbers 14.85/14.93 ->Dimension: 14.85/14.93 1 14.85/14.93 ->Bound: 14.85/14.93 2 14.85/14.93 ->Interpretation: 14.85/14.93 14.85/14.93 [0](X) = 2.X + 2 14.85/14.93 [1](X) = 2.X + 2 14.85/14.93 [2](X) = 2.X + 2 14.85/14.93 [5](X) = 2.X + 2 14.85/14.93 [3](X) = X 14.85/14.93 [4](X) = X 14.85/14.93 [0#](X) = 2.X + 2 14.85/14.93 [1#](X) = 2.X + 2 14.85/14.93 [2#](X) = 2.X + 2 14.85/14.93 [5#](X) = 2.X + 2 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 SCC Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Strongly Connected Components: 14.85/14.93 ->->Cycle: 14.85/14.93 ->->-> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 ->->-> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 Reduction Pair Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(1(4(2(5(x1:S))))) -> 5#(1(x1:S)) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 -> Usable rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Interpretation type: 14.85/14.93 Linear 14.85/14.93 ->Coefficients: 14.85/14.93 Natural Numbers 14.85/14.93 ->Dimension: 14.85/14.93 1 14.85/14.93 ->Bound: 14.85/14.93 2 14.85/14.93 ->Interpretation: 14.85/14.93 14.85/14.93 [0](X) = 2.X + 2 14.85/14.93 [1](X) = 2.X + 2 14.85/14.93 [2](X) = 2.X + 2 14.85/14.93 [5](X) = 2.X + 2 14.85/14.93 [3](X) = X 14.85/14.93 [4](X) = X 14.85/14.93 [0#](X) = 2.X 14.85/14.93 [1#](X) = 2.X + 1 14.85/14.93 [2#](X) = 2.X + 2 14.85/14.93 [5#](X) = 2.X + 2 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 SCC Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 ->Strongly Connected Components: 14.85/14.93 ->->Cycle: 14.85/14.93 ->->-> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 ->->-> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.93 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.93 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.93 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.93 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.93 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.93 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.93 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.93 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.93 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.93 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.93 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.93 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.93 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.93 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.93 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.93 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.93 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.93 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.93 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.93 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.93 14.85/14.93 Problem 1: 14.85/14.93 14.85/14.93 Reduction Pair Processor: 14.85/14.93 -> Pairs: 14.85/14.93 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.93 0#(2(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.93 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.93 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.93 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.93 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.93 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.93 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.93 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.93 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.93 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.93 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.93 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.93 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.93 -> Rules: 14.85/14.93 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.93 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.93 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.93 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.93 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.93 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.93 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.93 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.93 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.93 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.93 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.93 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.93 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.93 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.93 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.93 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.93 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.93 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.93 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.93 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.93 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.93 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.93 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 -> Usable rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Interpretation type: 14.85/14.94 Linear 14.85/14.94 ->Coefficients: 14.85/14.94 Natural Numbers 14.85/14.94 ->Dimension: 14.85/14.94 1 14.85/14.94 ->Bound: 14.85/14.94 2 14.85/14.94 ->Interpretation: 14.85/14.94 14.85/14.94 [0](X) = 2.X + 2 14.85/14.94 [1](X) = 2.X + 2 14.85/14.94 [2](X) = 2.X + 2 14.85/14.94 [5](X) = 2.X + 2 14.85/14.94 [3](X) = X 14.85/14.94 [4](X) = X 14.85/14.94 [0#](X) = 2.X + 1 14.85/14.94 [1#](X) = 2.X + 2 14.85/14.94 [2#](X) = 2.X + 1 14.85/14.94 [5#](X) = 2.X + 2 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 SCC Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Strongly Connected Components: 14.85/14.94 ->->Cycle: 14.85/14.94 ->->-> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 ->->-> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 Reduction Pair Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(5(2(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 -> Usable rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Interpretation type: 14.85/14.94 Linear 14.85/14.94 ->Coefficients: 14.85/14.94 Natural Numbers 14.85/14.94 ->Dimension: 14.85/14.94 1 14.85/14.94 ->Bound: 14.85/14.94 2 14.85/14.94 ->Interpretation: 14.85/14.94 14.85/14.94 [0](X) = 2.X + 2 14.85/14.94 [1](X) = 2.X + 2 14.85/14.94 [2](X) = 2.X + 2 14.85/14.94 [5](X) = 2.X + 2 14.85/14.94 [3](X) = X 14.85/14.94 [4](X) = X 14.85/14.94 [0#](X) = 2.X + 2 14.85/14.94 [1#](X) = 2.X + 2 14.85/14.94 [2#](X) = 2.X 14.85/14.94 [5#](X) = 2.X + 2 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 SCC Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Strongly Connected Components: 14.85/14.94 ->->Cycle: 14.85/14.94 ->->-> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 ->->-> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 Reduction Pair Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(5(2(x1:S)))) -> 5#(x1:S) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 -> Usable rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Interpretation type: 14.85/14.94 Linear 14.85/14.94 ->Coefficients: 14.85/14.94 Natural Numbers 14.85/14.94 ->Dimension: 14.85/14.94 1 14.85/14.94 ->Bound: 14.85/14.94 2 14.85/14.94 ->Interpretation: 14.85/14.94 14.85/14.94 [0](X) = X + 2 14.85/14.94 [1](X) = X + 2 14.85/14.94 [2](X) = X + 2 14.85/14.94 [5](X) = X + 2 14.85/14.94 [3](X) = X 14.85/14.94 [4](X) = X 14.85/14.94 [0#](X) = 2.X + 1 14.85/14.94 [1#](X) = 2.X + 2 14.85/14.94 [2#](X) = 2.X + 1 14.85/14.94 [5#](X) = 2.X + 2 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 SCC Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Strongly Connected Components: 14.85/14.94 ->->Cycle: 14.85/14.94 ->->-> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 ->->-> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 Reduction Pair Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(2(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 -> Usable rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Interpretation type: 14.85/14.94 Linear 14.85/14.94 ->Coefficients: 14.85/14.94 Natural Numbers 14.85/14.94 ->Dimension: 14.85/14.94 1 14.85/14.94 ->Bound: 14.85/14.94 2 14.85/14.94 ->Interpretation: 14.85/14.94 14.85/14.94 [0](X) = 2.X + 2 14.85/14.94 [1](X) = 2.X + 2 14.85/14.94 [2](X) = 2.X + 2 14.85/14.94 [5](X) = 2.X + 2 14.85/14.94 [3](X) = X 14.85/14.94 [4](X) = X 14.85/14.94 [0#](X) = 2.X + 2 14.85/14.94 [1#](X) = 2.X 14.85/14.94 [2#](X) = X 14.85/14.94 [5#](X) = 2.X 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 SCC Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Strongly Connected Components: 14.85/14.94 ->->Cycle: 14.85/14.94 ->->-> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 ->->-> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 Reduction Pair Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(5(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 -> Usable rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Interpretation type: 14.85/14.94 Linear 14.85/14.94 ->Coefficients: 14.85/14.94 Natural Numbers 14.85/14.94 ->Dimension: 14.85/14.94 1 14.85/14.94 ->Bound: 14.85/14.94 2 14.85/14.94 ->Interpretation: 14.85/14.94 14.85/14.94 [0](X) = 2.X + 2 14.85/14.94 [1](X) = 2.X + 2 14.85/14.94 [2](X) = 2.X + 2 14.85/14.94 [5](X) = 2.X + 2 14.85/14.94 [3](X) = X 14.85/14.94 [4](X) = X 14.85/14.94 [0#](X) = 2.X + 2 14.85/14.94 [1#](X) = 2.X 14.85/14.94 [2#](X) = 2.X + 2 14.85/14.94 [5#](X) = 2.X 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 SCC Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Strongly Connected Components: 14.85/14.94 ->->Cycle: 14.85/14.94 ->->-> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 ->->-> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 Reduction Pair Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 -> Usable rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Interpretation type: 14.85/14.94 Linear 14.85/14.94 ->Coefficients: 14.85/14.94 Natural Numbers 14.85/14.94 ->Dimension: 14.85/14.94 1 14.85/14.94 ->Bound: 14.85/14.94 2 14.85/14.94 ->Interpretation: 14.85/14.94 14.85/14.94 [0](X) = 2.X + 2 14.85/14.94 [1](X) = 2.X + 2 14.85/14.94 [2](X) = 2.X + 2 14.85/14.94 [5](X) = 2.X + 2 14.85/14.94 [3](X) = X 14.85/14.94 [4](X) = X 14.85/14.94 [0#](X) = 2.X + 1 14.85/14.94 [1#](X) = 2.X + 2 14.85/14.94 [2#](X) = 2.X + 2 14.85/14.94 [5#](X) = 2.X + 2 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 SCC Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Strongly Connected Components: 14.85/14.94 ->->Cycle: 14.85/14.94 ->->-> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 ->->-> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 Reduction Pair Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 1#(2(0(x1:S))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.94 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.94 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.94 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.94 -> Rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 -> Usable rules: 14.85/14.94 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.94 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.94 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.94 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.94 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.94 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.94 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.94 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.94 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.94 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.94 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.94 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.94 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.94 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.94 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.94 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.94 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.94 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.94 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.94 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.94 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.94 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.94 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.94 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.94 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.94 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.94 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.94 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.94 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.94 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.94 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.94 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.94 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.94 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.94 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.94 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.94 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.94 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.94 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.94 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.94 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.94 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.94 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.94 ->Interpretation type: 14.85/14.94 Linear 14.85/14.94 ->Coefficients: 14.85/14.94 Natural Numbers 14.85/14.94 ->Dimension: 14.85/14.94 1 14.85/14.94 ->Bound: 14.85/14.94 2 14.85/14.94 ->Interpretation: 14.85/14.94 14.85/14.94 [0](X) = 2.X + 1 14.85/14.94 [1](X) = 2.X + 1 14.85/14.94 [2](X) = 2.X + 1 14.85/14.94 [5](X) = 2.X + 1 14.85/14.94 [3](X) = X 14.85/14.94 [4](X) = X 14.85/14.94 [0#](X) = 2.X + 1 14.85/14.94 [1#](X) = 2.X + 2 14.85/14.94 [2#](X) = 2.X + 2 14.85/14.94 [5#](X) = 2.X + 2 14.85/14.94 14.85/14.94 Problem 1: 14.85/14.94 14.85/14.94 SCC Processor: 14.85/14.94 -> Pairs: 14.85/14.94 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.94 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.94 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.94 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.94 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.94 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.94 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.94 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.94 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.94 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.95 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.95 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.95 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 14.85/14.95 Problem 1: 14.85/14.95 14.85/14.95 Reduction Pair Processor: 14.85/14.95 -> Pairs: 14.85/14.95 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.95 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.95 0#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.95 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 -> Usable rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Interpretation type: 14.85/14.95 Linear 14.85/14.95 ->Coefficients: 14.85/14.95 Natural Numbers 14.85/14.95 ->Dimension: 14.85/14.95 1 14.85/14.95 ->Bound: 14.85/14.95 2 14.85/14.95 ->Interpretation: 14.85/14.95 14.85/14.95 [0](X) = X 14.85/14.95 [1](X) = 2.X + 2 14.85/14.95 [2](X) = 2.X + 2 14.85/14.95 [5](X) = X 14.85/14.95 [3](X) = X 14.85/14.95 [4](X) = X 14.85/14.95 [0#](X) = 2.X + 2 14.85/14.95 [1#](X) = 2.X + 2 14.85/14.95 [2#](X) = 2.X + 2 14.85/14.95 [5#](X) = 2.X + 2 14.85/14.95 14.85/14.95 Problem 1: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 0#(1(3(5(2(x1:S))))) -> 0#(4(1(5(2(x1:S))))) 14.85/14.95 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.95 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(4(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 2#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.95 2#(0(1(5(x1:S)))) -> 0#(5(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 1#(5(2(2(x1:S)))) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(0(4(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 1#(5(5(2(x1:S)))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 0#(5(1(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 1#(x1:S) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 0#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 1#(5(1(0(5(x1:S))))) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 0#(x1:S) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 14.85/14.95 14.85/14.95 The problem is decomposed in 3 subproblems. 14.85/14.95 14.85/14.95 Problem 1.1: 14.85/14.95 14.85/14.95 Reduction Pair Processor: 14.85/14.95 -> Pairs: 14.85/14.95 0#(4(0(2(1(x1:S))))) -> 0#(4(1(2(0(x1:S))))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 -> Usable rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Interpretation type: 14.85/14.95 Linear 14.85/14.95 ->Coefficients: 14.85/14.95 Natural Numbers 14.85/14.95 ->Dimension: 14.85/14.95 1 14.85/14.95 ->Bound: 14.85/14.95 2 14.85/14.95 ->Interpretation: 14.85/14.95 14.85/14.95 [0](X) = 2.X + 1 14.85/14.95 [1](X) = 2.X + 2 14.85/14.95 [2](X) = 2.X + 1 14.85/14.95 [5](X) = 2.X + 2 14.85/14.95 [3](X) = 0 14.85/14.95 [4](X) = X 14.85/14.95 [0#](X) = 2.X 14.85/14.95 14.85/14.95 Problem 1.1: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 Empty 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 There is no strongly connected component 14.85/14.95 14.85/14.95 The problem is finite. 14.85/14.95 14.85/14.95 Problem 1.2: 14.85/14.95 14.85/14.95 Reduction Pair Processor: 14.85/14.95 -> Pairs: 14.85/14.95 1#(0(0(1(5(x1:S))))) -> 1#(x1:S) 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 -> Usable rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Interpretation type: 14.85/14.95 Linear 14.85/14.95 ->Coefficients: 14.85/14.95 Natural Numbers 14.85/14.95 ->Dimension: 14.85/14.95 1 14.85/14.95 ->Bound: 14.85/14.95 2 14.85/14.95 ->Interpretation: 14.85/14.95 14.85/14.95 [0](X) = 2.X + 1 14.85/14.95 [1](X) = 2.X + 1 14.85/14.95 [2](X) = 2 14.85/14.95 [5](X) = 2.X + 1 14.85/14.95 [3](X) = 0 14.85/14.95 [4](X) = X 14.85/14.95 [1#](X) = 2.X 14.85/14.95 14.85/14.95 Problem 1.2: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 14.85/14.95 Problem 1.2: 14.85/14.95 14.85/14.95 Reduction Pair Processor: 14.85/14.95 -> Pairs: 14.85/14.95 1#(0(1(4(5(x1:S))))) -> 1#(0(5(x1:S))) 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 -> Usable rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Interpretation type: 14.85/14.95 Linear 14.85/14.95 ->Coefficients: 14.85/14.95 Natural Numbers 14.85/14.95 ->Dimension: 14.85/14.95 1 14.85/14.95 ->Bound: 14.85/14.95 2 14.85/14.95 ->Interpretation: 14.85/14.95 14.85/14.95 [0](X) = 2.X + 2 14.85/14.95 [1](X) = X + 2 14.85/14.95 [2](X) = 2 14.85/14.95 [5](X) = X + 1 14.85/14.95 [3](X) = 0 14.85/14.95 [4](X) = X + 1 14.85/14.95 [1#](X) = X 14.85/14.95 14.85/14.95 Problem 1.2: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 14.85/14.95 Problem 1.2: 14.85/14.95 14.85/14.95 Subterm Processor: 14.85/14.95 -> Pairs: 14.85/14.95 1#(1(4(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 1#(5(1(5(x1:S)))) -> 1#(x1:S) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Projection: 14.85/14.95 pi(1#) = 1 14.85/14.95 14.85/14.95 Problem 1.2: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 Empty 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 There is no strongly connected component 14.85/14.95 14.85/14.95 The problem is finite. 14.85/14.95 14.85/14.95 Problem 1.3: 14.85/14.95 14.85/14.95 Reduction Pair Processor: 14.85/14.95 -> Pairs: 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 2#(2(x1:S)) 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 -> Usable rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Interpretation type: 14.85/14.95 Linear 14.85/14.95 ->Coefficients: 14.85/14.95 Natural Numbers 14.85/14.95 ->Dimension: 14.85/14.95 1 14.85/14.95 ->Bound: 14.85/14.95 2 14.85/14.95 ->Interpretation: 14.85/14.95 14.85/14.95 [0](X) = 2.X + 2 14.85/14.95 [1](X) = X 14.85/14.95 [2](X) = 2.X + 2 14.85/14.95 [5](X) = 2.X + 2 14.85/14.95 [3](X) = X 14.85/14.95 [4](X) = X 14.85/14.95 [2#](X) = X + 2 14.85/14.95 [5#](X) = X + 2 14.85/14.95 14.85/14.95 Problem 1.3: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 14.85/14.95 Problem 1.3: 14.85/14.95 14.85/14.95 Reduction Pair Processor: 14.85/14.95 -> Pairs: 14.85/14.95 2#(0(5(1(2(x1:S))))) -> 5#(2(2(x1:S))) 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 -> Usable rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Interpretation type: 14.85/14.95 Linear 14.85/14.95 ->Coefficients: 14.85/14.95 Natural Numbers 14.85/14.95 ->Dimension: 14.85/14.95 1 14.85/14.95 ->Bound: 14.85/14.95 2 14.85/14.95 ->Interpretation: 14.85/14.95 14.85/14.95 [0](X) = 2.X 14.85/14.95 [1](X) = 2 14.85/14.95 [2](X) = 0 14.85/14.95 [5](X) = 2 14.85/14.95 [3](X) = 0 14.85/14.95 [4](X) = 2 14.85/14.95 [2#](X) = 2 14.85/14.95 [5#](X) = X 14.85/14.95 14.85/14.95 Problem 1.3: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 14.85/14.95 Problem 1.3: 14.85/14.95 14.85/14.95 Reduction Pair Processor: 14.85/14.95 -> Pairs: 14.85/14.95 2#(5(1(5(2(x1:S))))) -> 5#(5(2(x1:S))) 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 -> Usable rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Interpretation type: 14.85/14.95 Linear 14.85/14.95 ->Coefficients: 14.85/14.95 Natural Numbers 14.85/14.95 ->Dimension: 14.85/14.95 1 14.85/14.95 ->Bound: 14.85/14.95 2 14.85/14.95 ->Interpretation: 14.85/14.95 14.85/14.95 [0](X) = 2.X + 2 14.85/14.95 [1](X) = 2.X + 2 14.85/14.95 [2](X) = X 14.85/14.95 [5](X) = 2.X + 2 14.85/14.95 [3](X) = X 14.85/14.95 [4](X) = X 14.85/14.95 [2#](X) = 2.X 14.85/14.95 [5#](X) = X + 2 14.85/14.95 14.85/14.95 Problem 1.3: 14.85/14.95 14.85/14.95 SCC Processor: 14.85/14.95 -> Pairs: 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 2#(0(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 -> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.95 ->Strongly Connected Components: 14.85/14.95 ->->Cycle: 14.85/14.95 ->->-> Pairs: 14.85/14.95 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.95 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.95 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.95 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.95 ->->-> Rules: 14.85/14.95 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.95 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.95 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.95 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.95 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.95 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.95 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.95 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.95 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.95 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.95 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.95 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.95 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.95 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.95 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.95 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.95 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.95 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.95 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.95 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.95 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.95 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.95 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.95 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.95 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.95 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.95 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.95 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.95 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.95 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.95 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.95 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.95 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.95 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.95 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.95 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.95 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.95 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.95 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.95 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.95 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.95 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.95 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 Reduction Pair Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(0(1(2(x1:S)))) -> 5#(1(x1:S)) 14.85/14.96 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 -> Usable rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Interpretation type: 14.85/14.96 Linear 14.85/14.96 ->Coefficients: 14.85/14.96 Natural Numbers 14.85/14.96 ->Dimension: 14.85/14.96 1 14.85/14.96 ->Bound: 14.85/14.96 2 14.85/14.96 ->Interpretation: 14.85/14.96 14.85/14.96 [0](X) = 2.X + 1 14.85/14.96 [1](X) = 2 14.85/14.96 [2](X) = 1 14.85/14.96 [5](X) = 2 14.85/14.96 [3](X) = 0 14.85/14.96 [4](X) = 2 14.85/14.96 [5#](X) = 2.X 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 SCC Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Strongly Connected Components: 14.85/14.96 ->->Cycle: 14.85/14.96 ->->-> Pairs: 14.85/14.96 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 ->->-> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 Reduction Pair Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(0(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 -> Usable rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Interpretation type: 14.85/14.96 Linear 14.85/14.96 ->Coefficients: 14.85/14.96 Natural Numbers 14.85/14.96 ->Dimension: 14.85/14.96 1 14.85/14.96 ->Bound: 14.85/14.96 2 14.85/14.96 ->Interpretation: 14.85/14.96 14.85/14.96 [0](X) = 2.X + 2 14.85/14.96 [1](X) = 2.X + 2 14.85/14.96 [2](X) = 2.X + 2 14.85/14.96 [5](X) = 2.X + 2 14.85/14.96 [3](X) = 0 14.85/14.96 [4](X) = X 14.85/14.96 [5#](X) = X 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 SCC Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Strongly Connected Components: 14.85/14.96 ->->Cycle: 14.85/14.96 ->->-> Pairs: 14.85/14.96 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 ->->-> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 Reduction Pair Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(1(0(1(5(x1:S))))) -> 5#(1(0(5(x1:S)))) 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 -> Usable rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Interpretation type: 14.85/14.96 Linear 14.85/14.96 ->Coefficients: 14.85/14.96 Natural Numbers 14.85/14.96 ->Dimension: 14.85/14.96 1 14.85/14.96 ->Bound: 14.85/14.96 2 14.85/14.96 ->Interpretation: 14.85/14.96 14.85/14.96 [0](X) = 2.X + 2 14.85/14.96 [1](X) = 2.X + 2 14.85/14.96 [2](X) = 2.X + 2 14.85/14.96 [5](X) = 2.X 14.85/14.96 [3](X) = 0 14.85/14.96 [4](X) = X 14.85/14.96 [5#](X) = 2.X 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 SCC Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Strongly Connected Components: 14.85/14.96 ->->Cycle: 14.85/14.96 ->->-> Pairs: 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 ->->-> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 Reduction Pair Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(5(1(4(5(x1:S))))) -> 5#(5(x1:S)) 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 -> Usable rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Interpretation type: 14.85/14.96 Linear 14.85/14.96 ->Coefficients: 14.85/14.96 Natural Numbers 14.85/14.96 ->Dimension: 14.85/14.96 1 14.85/14.96 ->Bound: 14.85/14.96 2 14.85/14.96 ->Interpretation: 14.85/14.96 14.85/14.96 [0](X) = 2.X + 2 14.85/14.96 [1](X) = X 14.85/14.96 [2](X) = 2 14.85/14.96 [5](X) = 2.X + 2 14.85/14.96 [3](X) = 0 14.85/14.96 [4](X) = X 14.85/14.96 [5#](X) = X 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 SCC Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Strongly Connected Components: 14.85/14.96 ->->Cycle: 14.85/14.96 ->->-> Pairs: 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 ->->-> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 Reduction Pair Processor: 14.85/14.96 -> Pairs: 14.85/14.96 5#(4(0(2(1(x1:S))))) -> 5#(2(0(x1:S))) 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 -> Usable rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Interpretation type: 14.85/14.96 Linear 14.85/14.96 ->Coefficients: 14.85/14.96 Natural Numbers 14.85/14.96 ->Dimension: 14.85/14.96 1 14.85/14.96 ->Bound: 14.85/14.96 2 14.85/14.96 ->Interpretation: 14.85/14.96 14.85/14.96 [0](X) = X + 1 14.85/14.96 [1](X) = 2 14.85/14.96 [2](X) = 1 14.85/14.96 [5](X) = X 14.85/14.96 [3](X) = 0 14.85/14.96 [4](X) = 2 14.85/14.96 [5#](X) = 2.X 14.85/14.96 14.85/14.96 Problem 1.3: 14.85/14.96 14.85/14.96 SCC Processor: 14.85/14.96 -> Pairs: 14.85/14.96 Empty 14.85/14.96 -> Rules: 14.85/14.96 0(0(0(0(1(x1:S))))) -> 0(0(1(0(0(3(x1:S)))))) 14.85/14.96 0(0(0(2(x1:S)))) -> 3(0(0(3(0(2(x1:S)))))) 14.85/14.96 0(0(1(2(5(x1:S))))) -> 2(0(0(5(3(1(x1:S)))))) 14.85/14.96 0(0(1(5(2(x1:S))))) -> 0(1(0(3(5(2(x1:S)))))) 14.85/14.96 0(0(2(2(x1:S)))) -> 2(3(0(0(3(2(x1:S)))))) 14.85/14.96 0(1(0(4(5(x1:S))))) -> 5(4(0(0(3(1(x1:S)))))) 14.85/14.96 0(1(1(1(2(x1:S))))) -> 1(0(3(1(1(2(x1:S)))))) 14.85/14.96 0(1(1(2(x1:S)))) -> 2(3(0(3(1(1(x1:S)))))) 14.85/14.96 0(1(2(1(5(x1:S))))) -> 2(1(0(5(3(1(x1:S)))))) 14.85/14.96 0(1(2(1(x1:S)))) -> 0(1(2(4(1(3(x1:S)))))) 14.85/14.96 0(1(2(2(x1:S)))) -> 2(3(0(3(1(2(x1:S)))))) 14.85/14.96 0(1(2(5(x1:S)))) -> 2(0(5(3(1(x1:S))))) 14.85/14.96 0(1(2(x1:S))) -> 2(3(0(3(1(x1:S))))) 14.85/14.96 0(1(5(0(1(x1:S))))) -> 0(1(1(0(5(3(x1:S)))))) 14.85/14.96 0(1(5(0(5(x1:S))))) -> 3(5(1(0(5(0(x1:S)))))) 14.85/14.96 0(1(5(1(x1:S)))) -> 1(0(3(5(3(1(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(1(0(3(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 2(4(3(1(0(5(x1:S)))))) 14.85/14.96 0(1(5(2(x1:S)))) -> 3(1(3(0(5(2(x1:S)))))) 14.85/14.96 0(1(5(5(x1:S)))) -> 1(3(0(5(5(x1:S))))) 14.85/14.96 0(1(3(5(2(x1:S))))) -> 3(0(4(1(5(2(x1:S)))))) 14.85/14.96 0(1(4(2(5(x1:S))))) -> 2(4(3(0(5(1(x1:S)))))) 14.85/14.96 0(1(4(4(2(x1:S))))) -> 1(0(4(4(4(2(x1:S)))))) 14.85/14.96 0(2(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 0(2(5(2(x1:S)))) -> 2(2(3(0(5(x1:S))))) 14.85/14.96 0(2(4(2(1(x1:S))))) -> 2(1(2(4(3(0(x1:S)))))) 14.85/14.96 0(5(0(1(5(x1:S))))) -> 0(5(0(5(3(1(x1:S)))))) 14.85/14.96 0(4(0(2(1(x1:S))))) -> 3(0(4(1(2(0(x1:S)))))) 14.85/14.96 1(0(0(1(5(x1:S))))) -> 5(1(0(0(3(1(x1:S)))))) 14.85/14.96 1(0(1(4(5(x1:S))))) -> 1(4(4(1(0(5(x1:S)))))) 14.85/14.96 1(1(4(5(x1:S)))) -> 5(4(1(3(1(x1:S))))) 14.85/14.96 1(5(1(5(x1:S)))) -> 1(3(5(5(3(1(x1:S)))))) 14.85/14.96 1(5(5(1(x1:S)))) -> 1(5(3(1(5(3(x1:S)))))) 14.85/14.96 1(4(0(1(5(x1:S))))) -> 1(4(1(3(0(5(x1:S)))))) 14.85/14.96 2(0(1(2(x1:S)))) -> 2(2(3(0(3(1(x1:S)))))) 14.85/14.96 2(0(1(5(2(x1:S))))) -> 2(1(0(3(5(2(x1:S)))))) 14.85/14.96 2(0(1(5(x1:S)))) -> 2(1(3(0(5(x1:S))))) 14.85/14.96 2(0(5(1(2(x1:S))))) -> 0(3(1(5(2(2(x1:S)))))) 14.85/14.96 2(0(4(2(1(x1:S))))) -> 2(1(4(2(3(0(x1:S)))))) 14.85/14.96 2(2(1(1(2(x1:S))))) -> 2(2(1(3(1(2(x1:S)))))) 14.85/14.96 2(5(1(5(2(x1:S))))) -> 2(4(1(5(5(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 3(0(5(3(1(2(x1:S)))))) 14.85/14.96 5(0(1(2(x1:S)))) -> 4(2(3(0(5(1(x1:S)))))) 14.85/14.96 5(0(1(4(5(x1:S))))) -> 4(1(0(3(5(5(x1:S)))))) 14.85/14.96 5(1(0(1(5(x1:S))))) -> 3(1(5(1(0(5(x1:S)))))) 14.85/14.96 5(5(1(4(5(x1:S))))) -> 5(4(1(3(5(5(x1:S)))))) 14.85/14.96 5(4(0(2(1(x1:S))))) -> 4(1(3(5(2(0(x1:S)))))) 14.85/14.96 ->Strongly Connected Components: 14.85/14.96 There is no strongly connected component 14.85/14.96 14.85/14.96 The problem is finite. 14.85/14.96 EOF