7.34/7.27 YES 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 (VAR v_NonEmpty:S x1:S) 7.34/7.27 (RULES 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ) 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 Dependency Pairs Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(4(1(x1:S)))) -> 0#(3(0(3(x1:S)))) 7.34/7.27 0#(0(4(1(x1:S)))) -> 0#(3(x1:S)) 7.34/7.27 0#(0(4(1(x1:S)))) -> 4#(0(3(0(3(x1:S))))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(0(3(5(5(x1:S))))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(3(5(5(x1:S)))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 5#(5(x1:S)) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 5#(x1:S) 7.34/7.27 0#(0(5(1(x1:S)))) -> 0#(0(3(1(2(5(x1:S)))))) 7.34/7.27 0#(0(5(1(x1:S)))) -> 0#(3(1(2(5(x1:S))))) 7.34/7.27 0#(0(5(1(x1:S)))) -> 5#(x1:S) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(3(1(x1:S))) 7.34/7.27 0#(0(1(x1:S))) -> 0#(1(2(0(3(x1:S))))) 7.34/7.27 0#(0(1(x1:S))) -> 0#(3(x1:S)) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(3(0(1(x1:S)))) 7.34/7.27 0#(4(4(1(x1:S)))) -> 0#(3(4(1(x1:S)))) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 0#(3(1(x1:S))) 7.34/7.27 0#(4(1(x1:S))) -> 0#(3(x1:S)) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(2(1(2(0(3(x1:S)))))) 7.34/7.27 0#(5(0(1(x1:S)))) -> 0#(3(0(1(x1:S)))) 7.34/7.27 0#(5(0(1(x1:S)))) -> 5#(2(0(3(0(1(x1:S)))))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 0#(1(2(0(3(5(x1:S)))))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 0#(1(3(5(0(x1:S))))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 0#(3(5(x1:S))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 5#(0(x1:S)) 7.34/7.27 0#(5(1(0(x1:S)))) -> 5#(x1:S) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(1(5(2(0(0(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 5#(2(0(0(x1:S)))) 7.34/7.27 0#(1(0(x1:S))) -> 0#(3(1(2(0(x1:S))))) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(3(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 5#(0(0(3(x1:S)))) 7.34/7.27 0#(1(1(0(x1:S)))) -> 0#(0(1(2(x1:S)))) 7.34/7.27 0#(2(5(0(1(x1:S))))) -> 0#(3(5(0(1(x1:S))))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 0#(5(3(4(1(x1:S))))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(0(5(3(4(1(x1:S)))))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 5#(3(4(1(x1:S)))) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(0(x1:S)))) -> 4#(1(2(0(x1:S)))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 5#(0(x1:S)) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(3(5(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(x1:S)))) -> 5#(4(x1:S)) 7.34/7.27 4#(1(5(0(x1:S)))) -> 5#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 5#(4(x1:S)) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 5#(1(3(0(5(4(x1:S)))))) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 0#(2(1(3(4(x1:S))))) 7.34/7.27 4#(3(1(0(x1:S)))) -> 0#(3(x1:S)) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(2(0(3(x1:S)))) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 0#(3(2(4(x1:S)))) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 5#(1(0(3(2(4(x1:S)))))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 5#(0(1(0(x1:S)))) -> 0#(3(0(x1:S))) 7.34/7.27 5#(0(1(0(x1:S)))) -> 0#(3(5(1(2(0(x1:S)))))) 7.34/7.27 5#(0(1(0(x1:S)))) -> 5#(1(2(0(x1:S)))) 7.34/7.27 5#(0(1(0(x1:S)))) -> 5#(2(0(3(0(x1:S))))) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 SCC Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(4(1(x1:S)))) -> 0#(3(0(3(x1:S)))) 7.34/7.27 0#(0(4(1(x1:S)))) -> 0#(3(x1:S)) 7.34/7.27 0#(0(4(1(x1:S)))) -> 4#(0(3(0(3(x1:S))))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(0(3(5(5(x1:S))))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(3(5(5(x1:S)))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 5#(5(x1:S)) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 5#(x1:S) 7.34/7.27 0#(0(5(1(x1:S)))) -> 0#(0(3(1(2(5(x1:S)))))) 7.34/7.27 0#(0(5(1(x1:S)))) -> 0#(3(1(2(5(x1:S))))) 7.34/7.27 0#(0(5(1(x1:S)))) -> 5#(x1:S) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(3(1(x1:S))) 7.34/7.27 0#(0(1(x1:S))) -> 0#(1(2(0(3(x1:S))))) 7.34/7.27 0#(0(1(x1:S))) -> 0#(3(x1:S)) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(3(0(1(x1:S)))) 7.34/7.27 0#(4(4(1(x1:S)))) -> 0#(3(4(1(x1:S)))) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 0#(3(1(x1:S))) 7.34/7.27 0#(4(1(x1:S))) -> 0#(3(x1:S)) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(2(1(2(0(3(x1:S)))))) 7.34/7.27 0#(5(0(1(x1:S)))) -> 0#(3(0(1(x1:S)))) 7.34/7.27 0#(5(0(1(x1:S)))) -> 5#(2(0(3(0(1(x1:S)))))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 0#(1(2(0(3(5(x1:S)))))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 0#(1(3(5(0(x1:S))))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 0#(3(5(x1:S))) 7.34/7.27 0#(5(1(0(x1:S)))) -> 5#(0(x1:S)) 7.34/7.27 0#(5(1(0(x1:S)))) -> 5#(x1:S) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(1(5(2(0(0(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 5#(2(0(0(x1:S)))) 7.34/7.27 0#(1(0(x1:S))) -> 0#(3(1(2(0(x1:S))))) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(3(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 5#(0(0(3(x1:S)))) 7.34/7.27 0#(1(1(0(x1:S)))) -> 0#(0(1(2(x1:S)))) 7.34/7.27 0#(2(5(0(1(x1:S))))) -> 0#(3(5(0(1(x1:S))))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 0#(5(3(4(1(x1:S))))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(0(5(3(4(1(x1:S)))))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 5#(3(4(1(x1:S)))) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(0(x1:S)))) -> 4#(1(2(0(x1:S)))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 5#(0(x1:S)) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(3(5(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(x1:S)))) -> 5#(4(x1:S)) 7.34/7.27 4#(1(5(0(x1:S)))) -> 5#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 5#(4(x1:S)) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 5#(1(3(0(5(4(x1:S)))))) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 0#(2(1(3(4(x1:S))))) 7.34/7.27 4#(3(1(0(x1:S)))) -> 0#(3(x1:S)) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(2(0(3(x1:S)))) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 0#(3(2(4(x1:S)))) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 5#(1(0(3(2(4(x1:S)))))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 5#(0(1(0(x1:S)))) -> 0#(3(0(x1:S))) 7.34/7.27 5#(0(1(0(x1:S)))) -> 0#(3(5(1(2(0(x1:S)))))) 7.34/7.27 5#(0(1(0(x1:S)))) -> 5#(1(2(0(x1:S)))) 7.34/7.27 5#(0(1(0(x1:S)))) -> 5#(2(0(3(0(x1:S))))) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ->Strongly Connected Components: 7.34/7.27 ->->Cycle: 7.34/7.27 ->->-> Pairs: 7.34/7.27 0#(0(4(1(x1:S)))) -> 4#(0(3(0(3(x1:S))))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(0(3(5(5(x1:S))))) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 ->->-> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 Reduction Pair Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(4(1(x1:S)))) -> 4#(0(3(0(3(x1:S))))) 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(0(3(5(5(x1:S))))) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 -> Usable rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ->Interpretation type: 7.34/7.27 Linear 7.34/7.27 ->Coefficients: 7.34/7.27 Natural Numbers 7.34/7.27 ->Dimension: 7.34/7.27 1 7.34/7.27 ->Bound: 7.34/7.27 2 7.34/7.27 ->Interpretation: 7.34/7.27 7.34/7.27 [0](X) = 2.X + 2 7.34/7.27 [4](X) = 2.X + 2 7.34/7.27 [5](X) = X 7.34/7.27 [1](X) = 2.X + 2 7.34/7.27 [2](X) = X 7.34/7.27 [3](X) = X 7.34/7.27 [0#](X) = X + 2 7.34/7.27 [4#](X) = X + 2 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 SCC Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(0(3(5(5(x1:S))))) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ->Strongly Connected Components: 7.34/7.27 ->->Cycle: 7.34/7.27 ->->-> Pairs: 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(0(3(5(5(x1:S))))) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 ->->-> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 Reduction Pair Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(5(5(1(x1:S))))) -> 0#(0(3(5(5(x1:S))))) 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 -> Usable rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ->Interpretation type: 7.34/7.27 Linear 7.34/7.27 ->Coefficients: 7.34/7.27 Natural Numbers 7.34/7.27 ->Dimension: 7.34/7.27 1 7.34/7.27 ->Bound: 7.34/7.27 2 7.34/7.27 ->Interpretation: 7.34/7.27 7.34/7.27 [0](X) = X + 2 7.34/7.27 [4](X) = X + 2 7.34/7.27 [5](X) = X 7.34/7.27 [1](X) = X + 2 7.34/7.27 [2](X) = X 7.34/7.27 [3](X) = X 7.34/7.27 [0#](X) = 2.X + 2 7.34/7.27 [4#](X) = 2.X + 2 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 SCC Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ->Strongly Connected Components: 7.34/7.27 ->->Cycle: 7.34/7.27 ->->-> Pairs: 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 ->->-> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 Reduction Pair Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(1(1(x1:S)))) -> 0#(0(3(1(x1:S)))) 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 -> Usable rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ->Interpretation type: 7.34/7.27 Linear 7.34/7.27 ->Coefficients: 7.34/7.27 Natural Numbers 7.34/7.27 ->Dimension: 7.34/7.27 1 7.34/7.27 ->Bound: 7.34/7.27 2 7.34/7.27 ->Interpretation: 7.34/7.27 7.34/7.27 [0](X) = 2.X + 2 7.34/7.27 [4](X) = 2.X + 2 7.34/7.27 [5](X) = X 7.34/7.27 [1](X) = 2.X + 2 7.34/7.27 [2](X) = X 7.34/7.27 [3](X) = X 7.34/7.27 [0#](X) = 2.X + 2 7.34/7.27 [4#](X) = 2.X + 2 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 SCC Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 ->Strongly Connected Components: 7.34/7.27 ->->Cycle: 7.34/7.27 ->->-> Pairs: 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 ->->-> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 7.34/7.27 Problem 1: 7.34/7.27 7.34/7.27 Reduction Pair Processor: 7.34/7.27 -> Pairs: 7.34/7.27 0#(0(2(1(x1:S)))) -> 0#(1(x1:S)) 7.34/7.27 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.27 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.27 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.27 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.27 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.27 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.27 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.27 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.27 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.27 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.27 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.27 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.27 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.27 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.27 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.27 -> Rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.27 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.27 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.27 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.27 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.27 -> Usable rules: 7.34/7.27 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.27 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.27 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.27 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.27 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.27 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.27 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.27 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.27 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.27 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.27 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.27 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.27 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.27 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.27 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.27 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.27 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.27 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.27 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.27 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.27 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.27 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.27 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.27 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.27 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.27 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.27 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.27 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.27 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.27 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.27 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.27 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.27 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = 2.X + 2 7.34/7.28 [4](X) = 2.X + 2 7.34/7.28 [5](X) = X 7.34/7.28 [1](X) = 2.X + 2 7.34/7.28 [2](X) = X 7.34/7.28 [3](X) = X 7.34/7.28 [0#](X) = 2.X + 1 7.34/7.28 [4#](X) = 2.X + 1 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.28 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Strongly Connected Components: 7.34/7.28 ->->Cycle: 7.34/7.28 ->->-> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.28 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 ->->-> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 Reduction Pair Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 0#(1(0(5(0(x1:S))))) -> 0#(0(x1:S)) 7.34/7.28 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 -> Usable rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = 2.X + 2 7.34/7.28 [4](X) = 2.X + 2 7.34/7.28 [5](X) = X 7.34/7.28 [1](X) = 2.X + 2 7.34/7.28 [2](X) = X 7.34/7.28 [3](X) = X 7.34/7.28 [0#](X) = 2.X + 2 7.34/7.28 [4#](X) = 2.X + 2 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Strongly Connected Components: 7.34/7.28 ->->Cycle: 7.34/7.28 ->->-> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 ->->-> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 Reduction Pair Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 0#(1(5(0(x1:S)))) -> 0#(0(3(x1:S))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 -> Usable rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = X 7.34/7.28 [4](X) = 2 7.34/7.28 [5](X) = X 7.34/7.28 [1](X) = 2 7.34/7.28 [2](X) = 2 7.34/7.28 [3](X) = 1 7.34/7.28 [0#](X) = X 7.34/7.28 [4#](X) = 2 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 0#(1(4(3(x1:S)))) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Strongly Connected Components: 7.34/7.28 ->->Cycle: 7.34/7.28 ->->-> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 ->->-> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 Reduction Pair Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(4(1(0(5(x1:S))))) -> 4#(1(x1:S)) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 -> Usable rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = X + 2 7.34/7.28 [4](X) = X + 2 7.34/7.28 [5](X) = X 7.34/7.28 [1](X) = X + 2 7.34/7.28 [2](X) = X 7.34/7.28 [3](X) = X 7.34/7.28 [0#](X) = 2.X + 2 7.34/7.28 [4#](X) = 2.X + 2 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Strongly Connected Components: 7.34/7.28 ->->Cycle: 7.34/7.28 ->->-> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 ->->-> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 Reduction Pair Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(0(x1:S)))) -> 0#(4(1(2(0(x1:S))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 -> Usable rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = 2.X + 2 7.34/7.28 [4](X) = X 7.34/7.28 [5](X) = 2.X 7.34/7.28 [1](X) = X 7.34/7.28 [2](X) = 0 7.34/7.28 [3](X) = X 7.34/7.28 [0#](X) = 2.X + 2 7.34/7.28 [4#](X) = X 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Strongly Connected Components: 7.34/7.28 ->->Cycle: 7.34/7.28 ->->-> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 ->->-> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 Reduction Pair Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(4(1(x1:S)))) -> 4#(0(3(4(1(x1:S))))) 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 -> Usable rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = 2.X + 2 7.34/7.28 [4](X) = 2.X + 2 7.34/7.28 [5](X) = X 7.34/7.28 [1](X) = 2.X + 2 7.34/7.28 [2](X) = X 7.34/7.28 [3](X) = X 7.34/7.28 [0#](X) = 2.X + 2 7.34/7.28 [4#](X) = 2.X 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Strongly Connected Components: 7.34/7.28 ->->Cycle: 7.34/7.28 ->->-> Pairs: 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 ->->-> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 Reduction Pair Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(4(1(x1:S))) -> 4#(0(3(1(x1:S)))) 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 -> Usable rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = 2.X + 2 7.34/7.28 [4](X) = 2.X + 2 7.34/7.28 [5](X) = X 7.34/7.28 [1](X) = 2.X + 2 7.34/7.28 [2](X) = X 7.34/7.28 [3](X) = X 7.34/7.28 [0#](X) = 2.X + 2 7.34/7.28 [4#](X) = 2.X + 1 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Strongly Connected Components: 7.34/7.28 ->->Cycle: 7.34/7.28 ->->-> Pairs: 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 ->->-> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 Reduction Pair Processor: 7.34/7.28 -> Pairs: 7.34/7.28 0#(5(5(4(1(x1:S))))) -> 4#(1(0(5(5(3(x1:S)))))) 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 -> Usable rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.28 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.28 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.28 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.28 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.28 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.28 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.28 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.28 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.28 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.28 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.28 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.28 ->Interpretation type: 7.34/7.28 Linear 7.34/7.28 ->Coefficients: 7.34/7.28 Natural Numbers 7.34/7.28 ->Dimension: 7.34/7.28 1 7.34/7.28 ->Bound: 7.34/7.28 2 7.34/7.28 ->Interpretation: 7.34/7.28 7.34/7.28 [0](X) = 1 7.34/7.28 [4](X) = 1 7.34/7.28 [5](X) = X + 1 7.34/7.28 [1](X) = 0 7.34/7.28 [2](X) = 0 7.34/7.28 [3](X) = 2 7.34/7.28 [0#](X) = X 7.34/7.28 [4#](X) = 2 7.34/7.28 7.34/7.28 Problem 1: 7.34/7.28 7.34/7.28 SCC Processor: 7.34/7.28 -> Pairs: 7.34/7.28 4#(1(0(1(x1:S)))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(0(x1:S))) -> 0#(4(x1:S)) 7.34/7.28 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 0#(4(5(0(x1:S)))) 7.34/7.28 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.28 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 0#(5(4(x1:S))) 7.34/7.28 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 0#(4(x1:S)) 7.34/7.28 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.28 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.28 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.28 -> Rules: 7.34/7.28 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.28 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.28 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.28 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.28 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.28 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.28 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.28 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.28 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.28 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.28 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.28 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.28 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.28 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.28 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.28 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.28 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.28 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.28 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.28 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.28 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.28 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.28 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.28 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.28 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.28 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(0(1(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [4](X) = 2.X + 2 7.34/7.29 [5](X) = X 7.34/7.29 [1](X) = X 7.34/7.29 [2](X) = X 7.34/7.29 [3](X) = X 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(0(x1:S))) -> 4#(x1:S) 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = X + 2 7.34/7.29 [4](X) = X + 2 7.34/7.29 [5](X) = X 7.34/7.29 [1](X) = X + 2 7.34/7.29 [2](X) = X 7.34/7.29 [3](X) = X 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(0(0(x1:S))))) -> 4#(5(0(x1:S))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [4](X) = 2.X + 2 7.34/7.29 [5](X) = X 7.34/7.29 [1](X) = X 7.34/7.29 [2](X) = X 7.34/7.29 [3](X) = X 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(0(3(5(x1:S)))) 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [4](X) = X 7.34/7.29 [5](X) = 2.X 7.34/7.29 [1](X) = X 7.34/7.29 [2](X) = 0 7.34/7.29 [3](X) = X 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 Empty 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [5](X) = 2.X + 1 7.34/7.29 [1](X) = 2.X + 2 7.34/7.29 [3](X) = X 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(1(5(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 Empty 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [5](X) = 2.X 7.34/7.29 [1](X) = 2.X + 2 7.34/7.29 [3](X) = 2.X 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(0(1(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 Empty 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = X + 2 7.34/7.29 [5](X) = X 7.34/7.29 [1](X) = X + 2 7.34/7.29 [3](X) = X + 1 7.34/7.29 [4#](X) = X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(0(x1:S)))) -> 4#(x1:S) 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 Empty 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [5](X) = 2.X 7.34/7.29 [1](X) = 2.X + 2 7.34/7.29 [3](X) = 2.X + 2 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(5(0(x1:S))))) -> 4#(x1:S) 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 Empty 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [5](X) = 2.X + 2 7.34/7.29 [1](X) = 2.X + 2 7.34/7.29 [3](X) = 2.X + 2 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 ->Strongly Connected Components: 7.34/7.29 ->->Cycle: 7.34/7.29 ->->-> Pairs: 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 ->->-> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 Reduction Pair Processor: 7.34/7.29 -> Pairs: 7.34/7.29 4#(3(1(1(0(x1:S))))) -> 4#(3(x1:S)) 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.29 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.29 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.29 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.29 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.29 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.29 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.29 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.29 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.29 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.29 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.29 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.29 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.29 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.29 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.29 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.29 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.29 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.29 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.29 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.29 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.29 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.29 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.29 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.29 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.29 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.29 -> Usable rules: 7.34/7.29 Empty 7.34/7.29 ->Interpretation type: 7.34/7.29 Linear 7.34/7.29 ->Coefficients: 7.34/7.29 Natural Numbers 7.34/7.29 ->Dimension: 7.34/7.29 1 7.34/7.29 ->Bound: 7.34/7.29 2 7.34/7.29 ->Interpretation: 7.34/7.29 7.34/7.29 [0](X) = 2.X + 2 7.34/7.29 [1](X) = 2.X 7.34/7.29 [3](X) = 2.X 7.34/7.29 [4#](X) = 2.X 7.34/7.29 7.34/7.29 Problem 1: 7.34/7.29 7.34/7.29 SCC Processor: 7.34/7.29 -> Pairs: 7.34/7.29 Empty 7.34/7.29 -> Rules: 7.34/7.29 0(0(4(1(x1:S)))) -> 1(4(0(3(0(3(x1:S)))))) 7.34/7.29 0(0(5(5(1(x1:S))))) -> 1(0(0(3(5(5(x1:S)))))) 7.34/7.29 0(0(5(1(x1:S)))) -> 0(0(3(1(2(5(x1:S)))))) 7.34/7.29 0(0(1(1(x1:S)))) -> 1(2(0(0(3(1(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(2(x1:S)))))) 7.34/7.29 0(0(1(x1:S))) -> 0(1(2(0(3(x1:S))))) 7.34/7.29 0(0(1(x1:S))) -> 1(2(0(0(3(2(x1:S)))))) 7.34/7.29 0(0(2(1(x1:S)))) -> 2(2(0(3(0(1(x1:S)))))) 7.34/7.29 0(4(4(1(x1:S)))) -> 2(4(0(3(4(1(x1:S)))))) 7.34/7.29 0(4(1(0(x1:S)))) -> 0(4(0(1(2(x1:S))))) 7.34/7.29 0(4(1(4(1(x1:S))))) -> 4(4(0(1(2(1(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 4(0(3(1(x1:S)))) 7.34/7.29 0(4(1(x1:S))) -> 4(2(1(2(0(3(x1:S)))))) 7.34/7.29 0(4(1(x1:S))) -> 2(4(0(5(3(1(x1:S)))))) 7.34/7.30 0(4(1(x1:S))) -> 2(4(0(3(2(1(x1:S)))))) 7.34/7.30 0(4(2(1(x1:S)))) -> 4(0(3(5(1(2(x1:S)))))) 7.34/7.30 0(4(2(1(x1:S)))) -> 4(0(3(2(2(1(x1:S)))))) 7.34/7.30 0(5(0(1(x1:S)))) -> 0(2(0(3(5(1(x1:S)))))) 7.34/7.30 0(5(0(1(x1:S)))) -> 5(2(0(3(0(1(x1:S)))))) 7.34/7.30 0(5(5(4(1(x1:S))))) -> 4(1(0(5(5(3(x1:S)))))) 7.34/7.30 0(5(1(0(x1:S)))) -> 0(1(2(0(3(5(x1:S)))))) 7.34/7.30 0(5(1(0(x1:S)))) -> 2(0(1(3(5(0(x1:S)))))) 7.34/7.30 0(1(0(5(0(x1:S))))) -> 0(1(5(2(0(0(x1:S)))))) 7.34/7.30 0(1(0(x1:S))) -> 2(0(3(1(2(0(x1:S)))))) 7.34/7.30 0(1(4(1(x1:S)))) -> 0(1(2(4(1(2(x1:S)))))) 7.34/7.30 0(1(5(0(x1:S)))) -> 1(2(5(0(0(3(x1:S)))))) 7.34/7.30 0(1(1(0(x1:S)))) -> 1(2(0(0(1(2(x1:S)))))) 7.34/7.30 0(2(4(1(x1:S)))) -> 4(0(5(3(1(2(x1:S)))))) 7.34/7.30 0(2(5(0(1(x1:S))))) -> 2(0(3(5(0(1(x1:S)))))) 7.34/7.30 0(3(1(0(0(x1:S))))) -> 0(0(3(0(1(2(x1:S)))))) 7.34/7.30 4(0(5(1(x1:S)))) -> 1(4(0(5(3(2(x1:S)))))) 7.34/7.30 4(4(1(0(5(x1:S))))) -> 4(0(5(3(4(1(x1:S)))))) 7.34/7.30 4(1(0(0(x1:S)))) -> 0(4(1(2(0(x1:S))))) 7.34/7.30 4(1(0(1(x1:S)))) -> 1(1(2(0(4(x1:S))))) 7.34/7.30 4(1(0(x1:S))) -> 1(2(0(4(x1:S)))) 7.34/7.30 4(1(5(0(0(x1:S))))) -> 1(2(0(4(5(0(x1:S)))))) 7.34/7.30 4(1(5(0(x1:S)))) -> 1(4(0(3(5(x1:S))))) 7.34/7.30 4(1(5(0(x1:S)))) -> 1(2(0(5(4(x1:S))))) 7.34/7.30 4(1(5(5(0(x1:S))))) -> 5(1(3(0(5(4(x1:S)))))) 7.34/7.30 4(3(1(0(1(x1:S))))) -> 1(1(2(3(0(4(x1:S)))))) 7.34/7.30 4(3(1(0(x1:S)))) -> 1(4(2(0(3(x1:S))))) 7.34/7.30 4(3(1(0(x1:S)))) -> 2(0(2(1(3(4(x1:S)))))) 7.34/7.30 4(3(1(0(x1:S)))) -> 2(1(4(2(0(3(x1:S)))))) 7.34/7.30 4(3(1(0(x1:S)))) -> 2(2(4(0(1(3(x1:S)))))) 7.34/7.30 4(3(1(5(0(x1:S))))) -> 5(1(0(3(2(4(x1:S)))))) 7.34/7.30 4(3(1(1(0(x1:S))))) -> 1(2(0(1(4(3(x1:S)))))) 7.34/7.30 5(0(1(0(x1:S)))) -> 0(3(5(1(2(0(x1:S)))))) 7.34/7.30 5(0(1(0(x1:S)))) -> 1(5(2(0(3(0(x1:S)))))) 7.34/7.30 5(4(1(0(x1:S)))) -> 0(1(2(4(5(2(x1:S)))))) 7.34/7.30 ->Strongly Connected Components: 7.34/7.30 There is no strongly connected component 7.34/7.30 7.34/7.30 The problem is finite. 7.34/7.30 EOF