5.87/6.05 YES 5.87/6.05 5.87/6.05 Problem 1: 5.87/6.05 5.87/6.05 (VAR v_NonEmpty:S x1:S) 5.87/6.05 (RULES 5.87/6.05 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.05 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.05 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.05 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.05 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.05 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.05 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.05 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.05 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.05 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.05 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.05 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.05 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.05 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.05 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.05 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.05 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.05 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.05 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.05 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.05 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.05 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.05 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.05 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.05 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.05 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.05 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.05 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.05 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.05 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.05 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.05 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.05 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.05 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.05 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.05 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.05 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.05 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.05 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.05 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.05 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.05 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.05 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.05 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.05 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.05 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.05 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.05 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.05 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.05 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.05 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.05 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.05 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.05 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.05 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.05 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.05 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.05 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.05 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.05 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.05 ) 5.87/6.05 5.87/6.05 Problem 1: 5.87/6.05 5.87/6.05 Dependency Pairs Processor: 5.87/6.05 -> Pairs: 5.87/6.05 0#(0(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.05 0#(0(4(0(0(x1:S))))) -> 0#(4(2(0(0(0(x1:S)))))) 5.87/6.05 0#(0(4(0(0(x1:S))))) -> 4#(2(0(0(0(x1:S))))) 5.87/6.05 0#(0(4(1(x1:S)))) -> 0#(1(0(x1:S))) 5.87/6.05 0#(0(4(1(x1:S)))) -> 0#(2(1(4(2(0(x1:S)))))) 5.87/6.05 0#(0(4(1(x1:S)))) -> 0#(5(4(2(0(x1:S))))) 5.87/6.05 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.05 0#(0(4(1(x1:S)))) -> 1#(0(5(4(2(0(x1:S)))))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(4(2(0(x1:S)))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 4#(2(0(1(0(x1:S))))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 4#(2(0(x1:S))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(2(4(x1:S)))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(4(2(0(x1:S)))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(2(4(x1:S))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(4(2(0(0(x1:S))))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(0(2(4(x1:S)))))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(0(x1:S)))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(4(2(0(x1:S)))))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(x1:S))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(5(4(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(4(4(2(0(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(2(0(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(5(4(4(2(0(x1:S)))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(5(4(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(5(4(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(1(2(0(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(4(1(2(0(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(4(2(0(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(2(0(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(2(1(0(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(2(4(2(1(0(x1:S)))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(5(4(0(1(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 0#(2(3(4(4(0(x1:S)))))) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 4#(2(0(0(0(x1:S))))) 5.87/6.06 1#(4(4(0(0(x1:S))))) -> 1#(4(2(0(0(x1:S))))) 5.87/6.06 1#(4(4(0(0(x1:S))))) -> 4#(1(4(2(0(0(x1:S)))))) 5.87/6.06 1#(4(4(0(0(x1:S))))) -> 4#(2(0(0(x1:S)))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(2(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 4#(1(2(0(x1:S)))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 4#(4(1(2(0(x1:S))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(0(x1:S)))) -> 4#(4(2(0(1(x1:S))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 4#(2(0(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(2(4(x1:S))))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(2(1(4(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(2(4(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(2(1(4(x1:S))))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(2(4(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(2(1(4(1(x1:S))))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 4#(4(2(0(1(0(x1:S)))))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 4#(2(0(1(0(x1:S))))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(2(0(0(4(x1:S))))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(2(0(4(0(x1:S))))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(4(1(x1:S)))) -> 4#(2(0(4(1(x1:S))))) 5.87/6.06 4#(0(4(4(0(x1:S))))) -> 0#(4(2(4(0(x1:S))))) 5.87/6.06 4#(0(4(4(0(x1:S))))) -> 4#(0(4(2(4(0(x1:S)))))) 5.87/6.06 4#(0(4(4(0(x1:S))))) -> 4#(2(4(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 4#(2(0(1(1(0(x1:S)))))) 5.87/6.06 4#(1(3(4(0(x1:S))))) -> 1#(4(2(4(0(x1:S))))) 5.87/6.06 4#(1(3(4(0(x1:S))))) -> 4#(2(4(0(x1:S)))) 5.87/6.06 4#(4(0(0(1(x1:S))))) -> 0#(4(2(0(1(x1:S))))) 5.87/6.06 4#(4(0(0(1(x1:S))))) -> 4#(0(4(2(0(1(x1:S)))))) 5.87/6.06 4#(4(0(0(1(x1:S))))) -> 4#(2(0(1(x1:S)))) 5.87/6.06 4#(4(4(0(x1:S)))) -> 4#(2(4(4(0(x1:S))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(2(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(5(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(2(4(x1:S)))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(5(4(x1:S)))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(2(4(1(4(x1:S))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(2(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(5(4(1(5(4(x1:S)))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 1#(2(4(x1:S))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(1(2(4(x1:S)))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(1(2(4(x1:S))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 1#(4(2(0(0(x1:S))))) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 1#(4(2(3(0(0(x1:S)))))) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 4#(2(0(0(x1:S)))) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 4#(2(3(0(0(x1:S))))) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(4(5(3(0(1(x1:S)))))) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 4#(5(3(0(1(x1:S))))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(4(2(0(3(x1:S))))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(4(5(3(0(3(x1:S)))))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(4(5(x1:S))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(2(0(3(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(5(3(0(3(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(5(4(x1:S)))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(1(4(x1:S)))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(4(1(x1:S)))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(4(5(1(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(3(1(4(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(5(1(x1:S))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(5(4(x1:S))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(5(3(4(1(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(0(x1:S))))) -> 0#(5(2(3(0(x1:S))))) 5.87/6.06 4#(3(5(0(0(x1:S))))) -> 4#(0(5(2(3(0(x1:S)))))) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 4#(3(5(4(0(x1:S))))) -> 4#(2(0(x1:S))) 5.87/6.06 4#(3(5(4(0(x1:S))))) -> 4#(3(4(2(0(x1:S))))) 5.87/6.06 4#(3(5(4(1(x1:S))))) -> 4#(2(4(5(1(x1:S))))) 5.87/6.06 4#(3(5(4(1(x1:S))))) -> 4#(5(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 5.87/6.06 Problem 1: 5.87/6.06 5.87/6.06 SCC Processor: 5.87/6.06 -> Pairs: 5.87/6.06 0#(0(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 0#(0(4(0(0(x1:S))))) -> 0#(4(2(0(0(0(x1:S)))))) 5.87/6.06 0#(0(4(0(0(x1:S))))) -> 4#(2(0(0(0(x1:S))))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(1(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(2(1(4(2(0(x1:S)))))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(5(4(2(0(x1:S))))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(5(4(2(0(x1:S)))))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(4(2(0(x1:S)))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 4#(2(0(1(0(x1:S))))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 4#(2(0(x1:S))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(2(4(x1:S)))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(4(2(0(x1:S)))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(2(4(x1:S))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(4(2(0(0(x1:S))))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(0(2(4(x1:S)))))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(0(x1:S)))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(4(2(0(x1:S)))))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(2(0(x1:S))) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(5(4(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(4(4(2(0(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(2(0(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(5(4(4(2(0(x1:S)))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(5(4(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(5(4(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(1(2(0(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(4(1(2(0(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(4(2(0(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(2(0(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(2(1(0(x1:S)))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(2(4(2(1(0(x1:S)))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(5(4(0(1(x1:S))))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 0#(2(3(4(4(0(x1:S)))))) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 4#(2(0(0(0(x1:S))))) 5.87/6.06 1#(4(4(0(0(x1:S))))) -> 1#(4(2(0(0(x1:S))))) 5.87/6.06 1#(4(4(0(0(x1:S))))) -> 4#(1(4(2(0(0(x1:S)))))) 5.87/6.06 1#(4(4(0(0(x1:S))))) -> 4#(2(0(0(x1:S)))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(2(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 4#(1(2(0(x1:S)))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 4#(4(1(2(0(x1:S))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(0(x1:S)))) -> 4#(4(2(0(1(x1:S))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 4#(2(0(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(2(4(x1:S))))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(2(1(4(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(2(4(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(2(1(4(x1:S))))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(2(4(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(2(1(4(1(x1:S))))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 4#(4(2(0(1(0(x1:S)))))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 4#(2(0(1(0(x1:S))))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(2(0(0(4(x1:S))))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(2(0(4(0(x1:S))))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(4(1(x1:S)))) -> 4#(2(0(4(1(x1:S))))) 5.87/6.06 4#(0(4(4(0(x1:S))))) -> 0#(4(2(4(0(x1:S))))) 5.87/6.06 4#(0(4(4(0(x1:S))))) -> 4#(0(4(2(4(0(x1:S)))))) 5.87/6.06 4#(0(4(4(0(x1:S))))) -> 4#(2(4(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 4#(2(0(1(1(0(x1:S)))))) 5.87/6.06 4#(1(3(4(0(x1:S))))) -> 1#(4(2(4(0(x1:S))))) 5.87/6.06 4#(1(3(4(0(x1:S))))) -> 4#(2(4(0(x1:S)))) 5.87/6.06 4#(4(0(0(1(x1:S))))) -> 0#(4(2(0(1(x1:S))))) 5.87/6.06 4#(4(0(0(1(x1:S))))) -> 4#(0(4(2(0(1(x1:S)))))) 5.87/6.06 4#(4(0(0(1(x1:S))))) -> 4#(2(0(1(x1:S)))) 5.87/6.06 4#(4(4(0(x1:S)))) -> 4#(2(4(4(0(x1:S))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(2(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(5(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(2(4(x1:S)))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(5(4(x1:S)))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(2(4(1(4(x1:S))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(2(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(5(4(1(5(4(x1:S)))))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 1#(2(4(x1:S))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(1(2(4(x1:S)))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(1(2(4(x1:S))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 1#(4(2(0(0(x1:S))))) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 1#(4(2(3(0(0(x1:S)))))) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 4#(2(0(0(x1:S)))) 5.87/6.06 4#(3(1(0(0(x1:S))))) -> 4#(2(3(0(0(x1:S))))) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(4(5(3(0(1(x1:S)))))) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 4#(5(3(0(1(x1:S))))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(4(2(0(3(x1:S))))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(4(5(3(0(3(x1:S)))))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(4(5(x1:S))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(2(0(3(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 4#(5(3(0(3(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(5(4(x1:S)))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(1(4(x1:S)))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(4(1(x1:S)))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(4(5(1(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(2(3(1(4(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(5(1(x1:S))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(5(4(x1:S))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(5(3(4(1(x1:S))))) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(0(x1:S))))) -> 0#(5(2(3(0(x1:S))))) 5.87/6.06 4#(3(5(0(0(x1:S))))) -> 4#(0(5(2(3(0(x1:S)))))) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 4#(3(5(4(0(x1:S))))) -> 4#(2(0(x1:S))) 5.87/6.06 4#(3(5(4(0(x1:S))))) -> 4#(3(4(2(0(x1:S))))) 5.87/6.06 4#(3(5(4(1(x1:S))))) -> 4#(2(4(5(1(x1:S))))) 5.87/6.06 4#(3(5(4(1(x1:S))))) -> 4#(5(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 ->Strongly Connected Components: 5.87/6.06 ->->Cycle: 5.87/6.06 ->->-> Pairs: 5.87/6.06 0#(0(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(1(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 ->->-> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 5.87/6.06 Problem 1: 5.87/6.06 5.87/6.06 Reduction Pair Processor: 5.87/6.06 -> Pairs: 5.87/6.06 0#(0(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(1(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 -> Usable rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 ->Interpretation type: 5.87/6.06 Linear 5.87/6.06 ->Coefficients: 5.87/6.06 Natural Numbers 5.87/6.06 ->Dimension: 5.87/6.06 1 5.87/6.06 ->Bound: 5.87/6.06 2 5.87/6.06 ->Interpretation: 5.87/6.06 5.87/6.06 [0](X) = 2.X + 2 5.87/6.06 [1](X) = X 5.87/6.06 [4](X) = 2.X + 2 5.87/6.06 [2](X) = 0 5.87/6.06 [3](X) = X 5.87/6.06 [5](X) = X 5.87/6.06 [0#](X) = 2.X + 2 5.87/6.06 [1#](X) = 2.X + 2 5.87/6.06 [4#](X) = 2.X + 2 5.87/6.06 5.87/6.06 Problem 1: 5.87/6.06 5.87/6.06 SCC Processor: 5.87/6.06 -> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(1(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 ->Strongly Connected Components: 5.87/6.06 ->->Cycle: 5.87/6.06 ->->-> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(1(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 ->->-> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 5.87/6.06 Problem 1: 5.87/6.06 5.87/6.06 Reduction Pair Processor: 5.87/6.06 -> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(1(0(x1:S))) 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 -> Usable rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 ->Interpretation type: 5.87/6.06 Linear 5.87/6.06 ->Coefficients: 5.87/6.06 Natural Numbers 5.87/6.06 ->Dimension: 5.87/6.06 1 5.87/6.06 ->Bound: 5.87/6.06 2 5.87/6.06 ->Interpretation: 5.87/6.06 5.87/6.06 [0](X) = 2.X + 2 5.87/6.06 [1](X) = X 5.87/6.06 [4](X) = 2.X + 2 5.87/6.06 [2](X) = 0 5.87/6.06 [3](X) = X 5.87/6.06 [5](X) = X 5.87/6.06 [0#](X) = 2.X 5.87/6.06 [1#](X) = 2.X 5.87/6.06 [4#](X) = 2.X 5.87/6.06 5.87/6.06 Problem 1: 5.87/6.06 5.87/6.06 SCC Processor: 5.87/6.06 -> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 ->Strongly Connected Components: 5.87/6.06 ->->Cycle: 5.87/6.06 ->->-> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 ->->-> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 5.87/6.06 Problem 1: 5.87/6.06 5.87/6.06 Reduction Pair Processor: 5.87/6.06 -> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 -> Usable rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 ->Interpretation type: 5.87/6.06 Linear 5.87/6.06 ->Coefficients: 5.87/6.06 Natural Numbers 5.87/6.06 ->Dimension: 5.87/6.06 1 5.87/6.06 ->Bound: 5.87/6.06 2 5.87/6.06 ->Interpretation: 5.87/6.06 5.87/6.06 [0](X) = 2.X + 2 5.87/6.06 [1](X) = X 5.87/6.06 [4](X) = 2.X + 1 5.87/6.06 [2](X) = 0 5.87/6.06 [3](X) = X 5.87/6.06 [5](X) = X 5.87/6.06 [0#](X) = 2.X 5.87/6.06 [1#](X) = 2.X 5.87/6.06 [4#](X) = 2.X + 1 5.87/6.06 5.87/6.06 Problem 1: 5.87/6.06 5.87/6.06 SCC Processor: 5.87/6.06 -> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 -> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.06 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.06 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.06 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.06 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.06 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.06 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.06 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.06 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.06 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.06 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.06 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.06 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.06 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.06 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.06 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.06 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.06 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.06 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.06 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.06 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.06 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.06 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.06 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.06 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.06 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.06 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.06 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.06 ->Strongly Connected Components: 5.87/6.06 ->->Cycle: 5.87/6.06 ->->-> Pairs: 5.87/6.06 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.06 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.06 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.06 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.06 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.06 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.06 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.06 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.06 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.06 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.06 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.06 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.06 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.06 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.06 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.06 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.06 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.06 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.06 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.06 ->->-> Rules: 5.87/6.06 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.06 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.06 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.06 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.06 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.06 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.06 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.06 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.06 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.06 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.06 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 Reduction Pair Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(0(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.07 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 -> Usable rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Interpretation type: 5.87/6.07 Linear 5.87/6.07 ->Coefficients: 5.87/6.07 Natural Numbers 5.87/6.07 ->Dimension: 5.87/6.07 1 5.87/6.07 ->Bound: 5.87/6.07 2 5.87/6.07 ->Interpretation: 5.87/6.07 5.87/6.07 [0](X) = 2.X + 2 5.87/6.07 [1](X) = X 5.87/6.07 [4](X) = 2.X + 2 5.87/6.07 [2](X) = X 5.87/6.07 [3](X) = X 5.87/6.07 [5](X) = X 5.87/6.07 [0#](X) = 2.X + 2 5.87/6.07 [1#](X) = 2.X + 1 5.87/6.07 [4#](X) = 2.X + 2 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 SCC Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.07 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Strongly Connected Components: 5.87/6.07 ->->Cycle: 5.87/6.07 ->->-> Pairs: 5.87/6.07 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.07 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 ->->-> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 Reduction Pair Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(0(x1:S)))) -> 0#(0(x1:S)) 5.87/6.07 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 -> Usable rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Interpretation type: 5.87/6.07 Linear 5.87/6.07 ->Coefficients: 5.87/6.07 Natural Numbers 5.87/6.07 ->Dimension: 5.87/6.07 1 5.87/6.07 ->Bound: 5.87/6.07 2 5.87/6.07 ->Interpretation: 5.87/6.07 5.87/6.07 [0](X) = 2.X + 2 5.87/6.07 [1](X) = X 5.87/6.07 [4](X) = 2.X + 2 5.87/6.07 [2](X) = 0 5.87/6.07 [3](X) = X 5.87/6.07 [5](X) = X 5.87/6.07 [0#](X) = X + 1 5.87/6.07 [1#](X) = 2.X + 2 5.87/6.07 [4#](X) = 2.X + 2 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 SCC Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Strongly Connected Components: 5.87/6.07 ->->Cycle: 5.87/6.07 ->->-> Pairs: 5.87/6.07 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 ->->-> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 Reduction Pair Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 -> Usable rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Interpretation type: 5.87/6.07 Linear 5.87/6.07 ->Coefficients: 5.87/6.07 Natural Numbers 5.87/6.07 ->Dimension: 5.87/6.07 1 5.87/6.07 ->Bound: 5.87/6.07 2 5.87/6.07 ->Interpretation: 5.87/6.07 5.87/6.07 [0](X) = X + 2 5.87/6.07 [1](X) = X 5.87/6.07 [4](X) = X + 2 5.87/6.07 [2](X) = X 5.87/6.07 [3](X) = X 5.87/6.07 [5](X) = X 5.87/6.07 [0#](X) = 2.X + 2 5.87/6.07 [1#](X) = 2.X + 2 5.87/6.07 [4#](X) = 2.X + 2 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 SCC Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Strongly Connected Components: 5.87/6.07 ->->Cycle: 5.87/6.07 ->->-> Pairs: 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 ->->-> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 Reduction Pair Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 -> Usable rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Interpretation type: 5.87/6.07 Linear 5.87/6.07 ->Coefficients: 5.87/6.07 Natural Numbers 5.87/6.07 ->Dimension: 5.87/6.07 1 5.87/6.07 ->Bound: 5.87/6.07 2 5.87/6.07 ->Interpretation: 5.87/6.07 5.87/6.07 [0](X) = X + 2 5.87/6.07 [1](X) = X 5.87/6.07 [4](X) = X + 2 5.87/6.07 [2](X) = X 5.87/6.07 [3](X) = X 5.87/6.07 [5](X) = X 5.87/6.07 [0#](X) = 2.X + 1 5.87/6.07 [1#](X) = 2.X + 2 5.87/6.07 [4#](X) = 2.X + 2 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 SCC Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 -> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 ->Strongly Connected Components: 5.87/6.07 ->->Cycle: 5.87/6.07 ->->-> Pairs: 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.07 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.07 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.07 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.07 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.07 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.07 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.07 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.07 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.07 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.07 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.07 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.07 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.07 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.07 ->->-> Rules: 5.87/6.07 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.07 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.07 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.07 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.07 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.07 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.07 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.07 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.07 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.07 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.07 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.07 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.07 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.07 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.07 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.07 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.07 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.07 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.07 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.07 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.07 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.07 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.07 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.07 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.07 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.07 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.07 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.07 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.07 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.07 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.07 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.07 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.07 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.07 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.07 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.07 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.07 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.07 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.07 5.87/6.07 Problem 1: 5.87/6.07 5.87/6.07 Reduction Pair Processor: 5.87/6.07 -> Pairs: 5.87/6.07 0#(4(4(1(x1:S)))) -> 0#(x1:S) 5.87/6.07 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.07 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.07 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.07 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 -> Usable rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Interpretation type: 5.87/6.08 Linear 5.87/6.08 ->Coefficients: 5.87/6.08 Natural Numbers 5.87/6.08 ->Dimension: 5.87/6.08 1 5.87/6.08 ->Bound: 5.87/6.08 2 5.87/6.08 ->Interpretation: 5.87/6.08 5.87/6.08 [0](X) = X + 2 5.87/6.08 [1](X) = X 5.87/6.08 [4](X) = X + 2 5.87/6.08 [2](X) = X 5.87/6.08 [3](X) = X 5.87/6.08 [5](X) = X 5.87/6.08 [0#](X) = 2.X + 2 5.87/6.08 [1#](X) = 2.X + 2 5.87/6.08 [4#](X) = 2.X + 2 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 SCC Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Strongly Connected Components: 5.87/6.08 ->->Cycle: 5.87/6.08 ->->-> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 ->->-> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 Reduction Pair Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 1#(0(x1:S)) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 -> Usable rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Interpretation type: 5.87/6.08 Linear 5.87/6.08 ->Coefficients: 5.87/6.08 Natural Numbers 5.87/6.08 ->Dimension: 5.87/6.08 1 5.87/6.08 ->Bound: 5.87/6.08 2 5.87/6.08 ->Interpretation: 5.87/6.08 5.87/6.08 [0](X) = 2.X + 2 5.87/6.08 [1](X) = X 5.87/6.08 [4](X) = 2.X + 2 5.87/6.08 [2](X) = 0 5.87/6.08 [3](X) = X 5.87/6.08 [5](X) = X 5.87/6.08 [0#](X) = X + 2 5.87/6.08 [1#](X) = 2.X + 1 5.87/6.08 [4#](X) = 2.X + 1 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 SCC Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Strongly Connected Components: 5.87/6.08 ->->Cycle: 5.87/6.08 ->->-> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 ->->-> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 Reduction Pair Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(0(1(x1:S))) 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 -> Usable rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Interpretation type: 5.87/6.08 Linear 5.87/6.08 ->Coefficients: 5.87/6.08 Natural Numbers 5.87/6.08 ->Dimension: 5.87/6.08 1 5.87/6.08 ->Bound: 5.87/6.08 2 5.87/6.08 ->Interpretation: 5.87/6.08 5.87/6.08 [0](X) = 2.X + 2 5.87/6.08 [1](X) = X 5.87/6.08 [4](X) = 2.X + 2 5.87/6.08 [2](X) = X 5.87/6.08 [3](X) = X 5.87/6.08 [5](X) = X 5.87/6.08 [0#](X) = 2.X + 2 5.87/6.08 [1#](X) = 2.X + 2 5.87/6.08 [4#](X) = 2.X + 2 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 SCC Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Strongly Connected Components: 5.87/6.08 ->->Cycle: 5.87/6.08 ->->-> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 ->->-> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 Reduction Pair Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 -> Usable rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Interpretation type: 5.87/6.08 Linear 5.87/6.08 ->Coefficients: 5.87/6.08 Natural Numbers 5.87/6.08 ->Dimension: 5.87/6.08 1 5.87/6.08 ->Bound: 5.87/6.08 2 5.87/6.08 ->Interpretation: 5.87/6.08 5.87/6.08 [0](X) = X + 2 5.87/6.08 [1](X) = X 5.87/6.08 [4](X) = X + 2 5.87/6.08 [2](X) = X 5.87/6.08 [3](X) = X 5.87/6.08 [5](X) = X 5.87/6.08 [0#](X) = 2.X + 2 5.87/6.08 [1#](X) = 2.X + 2 5.87/6.08 [4#](X) = 2.X + 2 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 SCC Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 ->Strongly Connected Components: 5.87/6.08 ->->Cycle: 5.87/6.08 ->->-> Pairs: 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 ->->-> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.08 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.08 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.08 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.08 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.08 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.08 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.08 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.08 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.08 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.08 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.08 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.08 5.87/6.08 Problem 1: 5.87/6.08 5.87/6.08 Reduction Pair Processor: 5.87/6.08 -> Pairs: 5.87/6.08 0#(4(3(4(0(x1:S))))) -> 4#(4(0(x1:S))) 5.87/6.08 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.08 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.08 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.08 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.08 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.08 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.08 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.08 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.08 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.08 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.08 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.08 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.08 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.08 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.08 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.08 -> Rules: 5.87/6.08 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.08 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.08 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.08 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.08 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.08 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.08 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.08 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.08 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.08 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.08 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.08 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.08 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.08 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.08 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.08 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.08 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.08 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.08 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.08 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.08 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.08 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.08 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.08 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.08 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.08 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 -> Usable rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Interpretation type: 5.87/6.09 Linear 5.87/6.09 ->Coefficients: 5.87/6.09 Natural Numbers 5.87/6.09 ->Dimension: 5.87/6.09 1 5.87/6.09 ->Bound: 5.87/6.09 2 5.87/6.09 ->Interpretation: 5.87/6.09 5.87/6.09 [0](X) = X + 2 5.87/6.09 [1](X) = X 5.87/6.09 [4](X) = X + 2 5.87/6.09 [2](X) = X 5.87/6.09 [3](X) = X 5.87/6.09 [5](X) = X 5.87/6.09 [0#](X) = X + 2 5.87/6.09 [1#](X) = X + 1 5.87/6.09 [4#](X) = X + 2 5.87/6.09 5.87/6.09 Problem 1: 5.87/6.09 5.87/6.09 SCC Processor: 5.87/6.09 -> Pairs: 5.87/6.09 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.09 1#(4(4(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.09 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.09 1#(4(4(0(x1:S)))) -> 0#(1(x1:S)) 5.87/6.09 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 0#(1(0(4(x1:S)))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 0#(4(x1:S)) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 0#(1(0(x1:S))) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 0#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 0#(0(4(x1:S))) 5.87/6.09 4#(0(4(0(x1:S)))) -> 0#(4(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 0#(1(1(0(x1:S)))) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 0#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 0#(1(x1:S)) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(0(x1:S)))) -> 0#(4(4(5(x1:S)))) 5.87/6.09 4#(3(4(0(x1:S)))) -> 0#(3(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Strongly Connected Components: 5.87/6.09 ->->Cycle: 5.87/6.09 ->->-> Pairs: 5.87/6.09 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.09 ->->-> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->->Cycle: 5.87/6.09 ->->-> Pairs: 5.87/6.09 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.09 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 ->->-> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 5.87/6.09 5.87/6.09 The problem is decomposed in 2 subproblems. 5.87/6.09 5.87/6.09 Problem 1.1: 5.87/6.09 5.87/6.09 Subterm Processor: 5.87/6.09 -> Pairs: 5.87/6.09 0#(3(4(0(0(x1:S))))) -> 0#(0(0(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Projection: 5.87/6.09 pi(0#) = 1 5.87/6.09 5.87/6.09 Problem 1.1: 5.87/6.09 5.87/6.09 SCC Processor: 5.87/6.09 -> Pairs: 5.87/6.09 Empty 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Strongly Connected Components: 5.87/6.09 There is no strongly connected component 5.87/6.09 5.87/6.09 The problem is finite. 5.87/6.09 5.87/6.09 Problem 1.2: 5.87/6.09 5.87/6.09 Reduction Pair Processor: 5.87/6.09 -> Pairs: 5.87/6.09 1#(4(4(0(1(x1:S))))) -> 1#(4(4(1(2(0(x1:S)))))) 5.87/6.09 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 -> Usable rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Interpretation type: 5.87/6.09 Linear 5.87/6.09 ->Coefficients: 5.87/6.09 Natural Numbers 5.87/6.09 ->Dimension: 5.87/6.09 1 5.87/6.09 ->Bound: 5.87/6.09 2 5.87/6.09 ->Interpretation: 5.87/6.09 5.87/6.09 [0](X) = 2.X + 2 5.87/6.09 [1](X) = X 5.87/6.09 [4](X) = 2.X + 2 5.87/6.09 [2](X) = 0 5.87/6.09 [3](X) = X 5.87/6.09 [5](X) = X 5.87/6.09 [1#](X) = 2.X + 2 5.87/6.09 [4#](X) = 2.X + 2 5.87/6.09 5.87/6.09 Problem 1.2: 5.87/6.09 5.87/6.09 SCC Processor: 5.87/6.09 -> Pairs: 5.87/6.09 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Strongly Connected Components: 5.87/6.09 ->->Cycle: 5.87/6.09 ->->-> Pairs: 5.87/6.09 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 ->->-> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 5.87/6.09 Problem 1.2: 5.87/6.09 5.87/6.09 Reduction Pair Processor: 5.87/6.09 -> Pairs: 5.87/6.09 1#(4(4(0(x1:S)))) -> 1#(x1:S) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 -> Usable rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Interpretation type: 5.87/6.09 Linear 5.87/6.09 ->Coefficients: 5.87/6.09 Natural Numbers 5.87/6.09 ->Dimension: 5.87/6.09 1 5.87/6.09 ->Bound: 5.87/6.09 2 5.87/6.09 ->Interpretation: 5.87/6.09 5.87/6.09 [0](X) = X + 2 5.87/6.09 [1](X) = X 5.87/6.09 [4](X) = X + 2 5.87/6.09 [2](X) = X 5.87/6.09 [3](X) = X 5.87/6.09 [5](X) = X 5.87/6.09 [1#](X) = 2.X + 2 5.87/6.09 [4#](X) = 2.X + 2 5.87/6.09 5.87/6.09 Problem 1.2: 5.87/6.09 5.87/6.09 SCC Processor: 5.87/6.09 -> Pairs: 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Strongly Connected Components: 5.87/6.09 ->->Cycle: 5.87/6.09 ->->-> Pairs: 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 ->->-> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 5.87/6.09 Problem 1.2: 5.87/6.09 5.87/6.09 Reduction Pair Processor: 5.87/6.09 -> Pairs: 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(1(x1:S))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 -> Usable rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Interpretation type: 5.87/6.09 Linear 5.87/6.09 ->Coefficients: 5.87/6.09 Natural Numbers 5.87/6.09 ->Dimension: 5.87/6.09 1 5.87/6.09 ->Bound: 5.87/6.09 2 5.87/6.09 ->Interpretation: 5.87/6.09 5.87/6.09 [0](X) = X + 2 5.87/6.09 [1](X) = X 5.87/6.09 [4](X) = X + 2 5.87/6.09 [2](X) = X 5.87/6.09 [3](X) = X 5.87/6.09 [5](X) = X 5.87/6.09 [1#](X) = 2.X + 2 5.87/6.09 [4#](X) = 2.X + 2 5.87/6.09 5.87/6.09 Problem 1.2: 5.87/6.09 5.87/6.09 SCC Processor: 5.87/6.09 -> Pairs: 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 ->Strongly Connected Components: 5.87/6.09 ->->Cycle: 5.87/6.09 ->->-> Pairs: 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 ->->-> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.09 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.09 5.87/6.09 Problem 1.2: 5.87/6.09 5.87/6.09 Reduction Pair Processor: 5.87/6.09 -> Pairs: 5.87/6.09 1#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.09 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.09 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.09 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.09 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.09 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.09 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.09 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.09 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.09 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.09 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.09 -> Rules: 5.87/6.09 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.09 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.09 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.09 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.09 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.09 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.09 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.09 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.09 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.09 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.09 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.09 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.09 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.09 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.09 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.09 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.09 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.09 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.09 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.09 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.09 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.09 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.09 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.09 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.09 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.09 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.09 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.09 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.09 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.09 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.09 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.09 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.09 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.09 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.09 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.09 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.10 -> Usable rules: 5.87/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.87/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.87/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.87/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.87/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.87/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.87/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.87/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.87/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.87/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.87/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.87/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.87/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.87/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.87/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.87/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.87/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.87/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.87/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.87/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.87/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.87/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.87/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.87/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.87/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.87/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.87/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.87/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.87/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.87/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.87/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.87/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.87/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.87/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.87/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.87/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.87/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.87/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.87/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.87/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.87/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.87/6.10 ->Interpretation type: 5.87/6.10 Linear 5.87/6.10 ->Coefficients: 5.87/6.10 Natural Numbers 5.87/6.10 ->Dimension: 5.87/6.10 1 5.87/6.10 ->Bound: 5.87/6.10 2 5.87/6.10 ->Interpretation: 5.87/6.10 5.87/6.10 [0](X) = X + 2 5.87/6.10 [1](X) = X 5.87/6.10 [4](X) = X + 2 5.87/6.10 [2](X) = X 5.87/6.10 [3](X) = X 5.87/6.10 [5](X) = X 5.87/6.10 [1#](X) = 2.X + 2 5.87/6.10 [4#](X) = 2.X + 2 5.87/6.10 5.87/6.10 Problem 1.2: 5.87/6.10 5.87/6.10 SCC Processor: 5.87/6.10 -> Pairs: 5.87/6.10 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.87/6.10 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.87/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.87/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.87/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.87/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.87/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.87/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.87/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.87/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.87/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.87/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.87/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.87/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.87/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.87/6.10 -> Rules: 5.87/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.87/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.87/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.87/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.87/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.87/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.87/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.87/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.87/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.87/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.87/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.87/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Strongly Connected Components: 5.91/6.10 ->->Cycle: 5.91/6.10 ->->-> Pairs: 5.91/6.10 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.91/6.10 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 ->->-> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 Reduction Pair Processor: 5.91/6.10 -> Pairs: 5.91/6.10 1#(4(4(1(x1:S)))) -> 4#(1(4(1(x1:S)))) 5.91/6.10 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 -> Usable rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Interpretation type: 5.91/6.10 Linear 5.91/6.10 ->Coefficients: 5.91/6.10 Natural Numbers 5.91/6.10 ->Dimension: 5.91/6.10 1 5.91/6.10 ->Bound: 5.91/6.10 2 5.91/6.10 ->Interpretation: 5.91/6.10 5.91/6.10 [0](X) = X + 2 5.91/6.10 [1](X) = X 5.91/6.10 [4](X) = X + 2 5.91/6.10 [2](X) = X 5.91/6.10 [3](X) = X 5.91/6.10 [5](X) = X 5.91/6.10 [1#](X) = 2.X + 1 5.91/6.10 [4#](X) = 2.X + 2 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 SCC Processor: 5.91/6.10 -> Pairs: 5.91/6.10 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Strongly Connected Components: 5.91/6.10 ->->Cycle: 5.91/6.10 ->->-> Pairs: 5.91/6.10 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 ->->-> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 Reduction Pair Processor: 5.91/6.10 -> Pairs: 5.91/6.10 1#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 -> Usable rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Interpretation type: 5.91/6.10 Linear 5.91/6.10 ->Coefficients: 5.91/6.10 Natural Numbers 5.91/6.10 ->Dimension: 5.91/6.10 1 5.91/6.10 ->Bound: 5.91/6.10 2 5.91/6.10 ->Interpretation: 5.91/6.10 5.91/6.10 [0](X) = X + 2 5.91/6.10 [1](X) = X 5.91/6.10 [4](X) = X + 2 5.91/6.10 [2](X) = X 5.91/6.10 [3](X) = X 5.91/6.10 [5](X) = X 5.91/6.10 [1#](X) = 2.X 5.91/6.10 [4#](X) = 2.X 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 SCC Processor: 5.91/6.10 -> Pairs: 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Strongly Connected Components: 5.91/6.10 ->->Cycle: 5.91/6.10 ->->-> Pairs: 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 ->->-> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 Reduction Pair Processor: 5.91/6.10 -> Pairs: 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 1#(4(4(1(x1:S)))) 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 -> Usable rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Interpretation type: 5.91/6.10 Linear 5.91/6.10 ->Coefficients: 5.91/6.10 Natural Numbers 5.91/6.10 ->Dimension: 5.91/6.10 1 5.91/6.10 ->Bound: 5.91/6.10 2 5.91/6.10 ->Interpretation: 5.91/6.10 5.91/6.10 [0](X) = X + 2 5.91/6.10 [1](X) = X 5.91/6.10 [4](X) = X + 2 5.91/6.10 [2](X) = X 5.91/6.10 [3](X) = X 5.91/6.10 [5](X) = X 5.91/6.10 [1#](X) = 2.X + 2 5.91/6.10 [4#](X) = 2.X + 2 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 SCC Processor: 5.91/6.10 -> Pairs: 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Strongly Connected Components: 5.91/6.10 ->->Cycle: 5.91/6.10 ->->-> Pairs: 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 ->->-> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 Reduction Pair Processor: 5.91/6.10 -> Pairs: 5.91/6.10 1#(4(4(4(1(x1:S))))) -> 4#(1(4(4(1(x1:S))))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 -> Usable rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Interpretation type: 5.91/6.10 Linear 5.91/6.10 ->Coefficients: 5.91/6.10 Natural Numbers 5.91/6.10 ->Dimension: 5.91/6.10 1 5.91/6.10 ->Bound: 5.91/6.10 2 5.91/6.10 ->Interpretation: 5.91/6.10 5.91/6.10 [0](X) = 2.X + 2 5.91/6.10 [1](X) = X 5.91/6.10 [4](X) = 2.X + 2 5.91/6.10 [2](X) = 0 5.91/6.10 [3](X) = X 5.91/6.10 [5](X) = X 5.91/6.10 [1#](X) = 2.X + 1 5.91/6.10 [4#](X) = 2.X + 2 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 SCC Processor: 5.91/6.10 -> Pairs: 5.91/6.10 4#(0(0(1(x1:S)))) -> 1#(0(4(x1:S))) 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(0(4(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(0(x1:S)) 5.91/6.10 4#(1(0(0(1(x1:S))))) -> 1#(1(0(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(1(5(0(x1:S))))) -> 1#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 1#(4(x1:S)) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 ->Strongly Connected Components: 5.91/6.10 ->->Cycle: 5.91/6.10 ->->-> Pairs: 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 ->->-> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.10 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.10 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.10 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.10 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.10 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.10 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.10 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.10 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.10 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.10 5.91/6.10 Problem 1.2: 5.91/6.10 5.91/6.10 Reduction Pair Processor: 5.91/6.10 -> Pairs: 5.91/6.10 4#(0(0(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.10 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.10 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.10 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.10 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.10 -> Rules: 5.91/6.10 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.10 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.10 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.10 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.10 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.10 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.10 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.10 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.10 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.10 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.10 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.10 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.10 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.10 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.10 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.10 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.10 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.10 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.10 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.10 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.10 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.10 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.10 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.10 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.10 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.10 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.10 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.10 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.10 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 -> Usable rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Interpretation type: 5.91/6.11 Linear 5.91/6.11 ->Coefficients: 5.91/6.11 Natural Numbers 5.91/6.11 ->Dimension: 5.91/6.11 1 5.91/6.11 ->Bound: 5.91/6.11 2 5.91/6.11 ->Interpretation: 5.91/6.11 5.91/6.11 [0](X) = X + 2 5.91/6.11 [1](X) = X 5.91/6.11 [4](X) = 2.X + 1 5.91/6.11 [2](X) = 0 5.91/6.11 [3](X) = X 5.91/6.11 [5](X) = X 5.91/6.11 [4#](X) = 2.X 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 SCC Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Strongly Connected Components: 5.91/6.11 ->->Cycle: 5.91/6.11 ->->-> Pairs: 5.91/6.11 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 ->->-> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 Reduction Pair Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(0(4(0(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 -> Usable rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Interpretation type: 5.91/6.11 Linear 5.91/6.11 ->Coefficients: 5.91/6.11 Natural Numbers 5.91/6.11 ->Dimension: 5.91/6.11 1 5.91/6.11 ->Bound: 5.91/6.11 2 5.91/6.11 ->Interpretation: 5.91/6.11 5.91/6.11 [0](X) = 2.X + 2 5.91/6.11 [1](X) = X 5.91/6.11 [4](X) = 2.X + 2 5.91/6.11 [2](X) = 0 5.91/6.11 [3](X) = X 5.91/6.11 [5](X) = X 5.91/6.11 [4#](X) = X 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 SCC Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Strongly Connected Components: 5.91/6.11 ->->Cycle: 5.91/6.11 ->->-> Pairs: 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 ->->-> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 Reduction Pair Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(1(4(x1:S))) 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 -> Usable rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Interpretation type: 5.91/6.11 Linear 5.91/6.11 ->Coefficients: 5.91/6.11 Natural Numbers 5.91/6.11 ->Dimension: 5.91/6.11 1 5.91/6.11 ->Bound: 5.91/6.11 2 5.91/6.11 ->Interpretation: 5.91/6.11 5.91/6.11 [0](X) = 2.X + 2 5.91/6.11 [1](X) = X 5.91/6.11 [4](X) = 2.X + 2 5.91/6.11 [2](X) = 0 5.91/6.11 [3](X) = X 5.91/6.11 [5](X) = X 5.91/6.11 [4#](X) = X 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 SCC Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Strongly Connected Components: 5.91/6.11 ->->Cycle: 5.91/6.11 ->->-> Pairs: 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 ->->-> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 Reduction Pair Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(4(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 -> Usable rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Interpretation type: 5.91/6.11 Linear 5.91/6.11 ->Coefficients: 5.91/6.11 Natural Numbers 5.91/6.11 ->Dimension: 5.91/6.11 1 5.91/6.11 ->Bound: 5.91/6.11 2 5.91/6.11 ->Interpretation: 5.91/6.11 5.91/6.11 [0](X) = 2 5.91/6.11 [1](X) = X 5.91/6.11 [4](X) = X + 1 5.91/6.11 [2](X) = 0 5.91/6.11 [3](X) = X + 1 5.91/6.11 [5](X) = 1 5.91/6.11 [4#](X) = 2.X 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 SCC Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(4(4(1(2(4(x1:S)))))) 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Strongly Connected Components: 5.91/6.11 ->->Cycle: 5.91/6.11 ->->-> Pairs: 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 ->->-> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 Subterm Processor: 5.91/6.11 -> Pairs: 5.91/6.11 4#(4(4(4(1(x1:S))))) -> 4#(x1:S) 5.91/6.11 4#(3(4(1(x1:S)))) -> 4#(x1:S) 5.91/6.11 4#(3(5(0(1(x1:S))))) -> 4#(0(1(x1:S))) 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Projection: 5.91/6.11 pi(4#) = 1 5.91/6.11 5.91/6.11 Problem 1.2: 5.91/6.11 5.91/6.11 SCC Processor: 5.91/6.11 -> Pairs: 5.91/6.11 Empty 5.91/6.11 -> Rules: 5.91/6.11 0(0(0(1(x1:S)))) -> 0(1(0(0(2(3(x1:S)))))) 5.91/6.11 0(0(4(0(0(x1:S))))) -> 0(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 0(2(1(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 1(0(5(4(2(0(x1:S)))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 4(2(0(1(0(x1:S))))) 5.91/6.11 0(0(4(1(x1:S)))) -> 3(4(2(0(1(0(x1:S)))))) 5.91/6.11 0(1(3(5(0(x1:S))))) -> 0(1(3(0(5(3(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 0(4(0(2(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(4(2(0(0(x1:S))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(4(2(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(0(2(4(x1:S)))))) 5.91/6.11 0(4(4(0(x1:S)))) -> 4(2(0(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(3(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(4(4(2(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 0(1(5(4(4(2(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(4(4(2(0(x1:S))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 1(5(4(4(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 4(2(4(2(1(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(0(1(5(4(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(4(1(2(0(x1:S)))))) 5.91/6.11 0(4(4(1(x1:S)))) -> 2(4(5(4(0(1(x1:S)))))) 5.91/6.11 0(4(3(4(0(x1:S))))) -> 0(2(3(4(4(0(x1:S)))))) 5.91/6.11 0(3(4(0(0(x1:S))))) -> 3(4(2(0(0(0(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(4(5(3(0(5(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(0(2(4(2(x1:S)))))) 5.91/6.11 0(3(4(0(x1:S)))) -> 0(3(4(2(0(2(x1:S)))))) 5.91/6.11 0(3(5(0(1(x1:S))))) -> 0(1(0(5(2(3(x1:S)))))) 5.91/6.11 0(3(5(4(1(x1:S))))) -> 5(1(0(4(5(3(x1:S)))))) 5.91/6.11 1(4(4(0(0(x1:S))))) -> 4(1(4(2(0(0(x1:S)))))) 5.91/6.11 1(4(4(0(1(x1:S))))) -> 1(4(4(1(2(0(x1:S)))))) 5.91/6.11 1(4(4(0(x1:S)))) -> 5(4(4(2(0(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(1(4(1(2(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(1(2(1(4(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(4(2(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(1(x1:S)))) -> 2(3(4(1(4(1(x1:S)))))) 5.91/6.11 1(4(4(4(1(x1:S))))) -> 2(4(1(4(4(1(x1:S)))))) 5.91/6.11 4(0(0(0(x1:S)))) -> 0(4(2(0(0(5(x1:S)))))) 5.91/6.11 4(0(0(1(x1:S)))) -> 2(3(0(1(0(4(x1:S)))))) 5.91/6.11 4(0(0(4(1(x1:S))))) -> 4(4(2(0(1(0(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 2(4(2(0(0(4(x1:S)))))) 5.91/6.11 4(0(4(0(x1:S)))) -> 3(4(2(0(4(0(x1:S)))))) 5.91/6.11 4(0(4(1(x1:S)))) -> 2(4(2(0(4(1(x1:S)))))) 5.91/6.11 4(0(4(4(0(x1:S))))) -> 4(0(4(2(4(0(x1:S)))))) 5.91/6.11 4(1(0(0(1(x1:S))))) -> 4(2(0(1(1(0(x1:S)))))) 5.91/6.11 4(1(3(4(0(x1:S))))) -> 3(1(4(2(4(0(x1:S)))))) 5.91/6.11 4(4(0(0(1(x1:S))))) -> 4(0(4(2(0(1(x1:S)))))) 5.91/6.11 4(4(4(0(x1:S)))) -> 2(4(2(4(4(0(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(2(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 4(5(4(1(5(4(x1:S)))))) 5.91/6.11 4(4(4(1(x1:S)))) -> 2(4(2(4(1(4(x1:S)))))) 5.91/6.11 4(4(4(4(1(x1:S))))) -> 4(4(4(1(2(4(x1:S)))))) 5.91/6.11 4(4(5(0(1(x1:S))))) -> 4(5(0(1(4(2(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 1(4(2(3(0(0(x1:S)))))) 5.91/6.11 4(3(1(0(0(x1:S))))) -> 3(1(4(2(0(0(x1:S)))))) 5.91/6.11 4(3(1(5(0(x1:S))))) -> 1(4(5(3(0(1(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 0(4(2(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(0(3(4(2(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(0(3(x1:S))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(2(3(0(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(4(5(3(0(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(2(0(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 4(3(0(5(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(4(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(0(4(4(5(x1:S)))))) 5.91/6.11 4(3(4(0(x1:S)))) -> 2(3(4(4(0(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 1(4(2(4(2(3(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(4(2(3(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(1(4(5(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 2(3(4(2(1(4(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(1(4(2(4(2(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(1(x1:S))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(4(1(x1:S)))) -> 3(4(5(3(4(1(x1:S)))))) 5.91/6.11 4(3(4(4(1(x1:S))))) -> 4(4(3(1(4(2(x1:S)))))) 5.91/6.11 4(3(2(4(0(x1:S))))) -> 4(2(0(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(0(0(x1:S))))) -> 4(0(5(2(3(0(x1:S)))))) 5.91/6.11 4(3(5(0(1(x1:S))))) -> 2(3(5(4(0(1(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(4(5(3(4(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 0(3(4(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 4(4(5(3(0(2(x1:S)))))) 5.91/6.11 4(3(5(4(0(x1:S))))) -> 5(4(3(4(2(0(x1:S)))))) 5.91/6.11 4(3(5(4(1(x1:S))))) -> 3(4(2(4(5(1(x1:S)))))) 5.91/6.11 4(3(5(5(0(x1:S))))) -> 0(2(3(5(4(5(x1:S)))))) 5.91/6.11 4(3(5(5(1(x1:S))))) -> 1(5(4(2(5(3(x1:S)))))) 5.91/6.11 ->Strongly Connected Components: 5.91/6.11 There is no strongly connected component 5.91/6.11 5.91/6.11 The problem is finite. 5.91/6.11 EOF