YES Problem: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) Proof: DP Processor: DPs: 2#(5(x1)) -> 1#(0(x1)) 2#(5(x1)) -> 3#(0(1(0(x1)))) 2#(5(x1)) -> 3#(3(0(1(0(x1))))) 2#(5(x1)) -> 1#(3(3(0(1(0(x1)))))) 2#(5(x1)) -> 1#(x1) 2#(5(x1)) -> 5#(0(1(x1))) 2#(5(x1)) -> 2#(0(5(0(1(x1))))) 2#(5(x1)) -> 2#(2(0(5(0(1(x1)))))) 3#(5(x1)) -> 1#(x1) 3#(5(x1)) -> 2#(0(0(1(x1)))) 3#(5(x1)) -> 3#(2(0(0(1(x1))))) 3#(5(x1)) -> 1#(3(2(0(0(1(x1)))))) 3#(5(x1)) -> 3#(0(x1)) 3#(5(x1)) -> 5#(3(0(x1))) 3#(5(x1)) -> 2#(0(5(3(0(x1))))) 3#(5(x1)) -> 3#(2(0(5(3(0(x1)))))) 4#(5(x1)) -> 1#(x1) 4#(5(x1)) -> 2#(1(x1)) 4#(5(x1)) -> 3#(2(1(x1))) 4#(5(x1)) -> 1#(3(2(1(x1)))) 4#(5(x1)) -> 2#(1(3(2(1(x1))))) 4#(5(x1)) -> 2#(2(1(3(2(1(x1)))))) 4#(5(x1)) -> 5#(0(0(x1))) 4#(5(x1)) -> 2#(0(5(0(0(x1))))) 4#(5(x1)) -> 3#(2(0(5(0(0(x1)))))) 1#(2(5(x1))) -> 4#(x1) 1#(2(5(x1))) -> 5#(4(x1)) 1#(2(5(x1))) -> 5#(0(5(4(x1)))) 1#(2(5(x1))) -> 1#(0(5(0(5(4(x1)))))) 1#(2(5(x1))) -> 1#(x1) 1#(2(5(x1))) -> 1#(0(1(x1))) 1#(2(5(x1))) -> 2#(1(0(1(x1)))) 1#(2(5(x1))) -> 2#(2(1(0(1(x1))))) 1#(2(5(x1))) -> 1#(2(2(1(0(1(x1)))))) 1#(2(5(x1))) -> 1#(0(x1)) 1#(2(5(x1))) -> 3#(1(0(x1))) 1#(2(5(x1))) -> 1#(3(1(0(x1)))) 1#(2(5(x1))) -> 2#(0(1(3(1(0(x1)))))) 1#(4(5(x1))) -> 1#(x1) 1#(4(5(x1))) -> 2#(1(x1)) 1#(4(5(x1))) -> 4#(0(2(1(x1)))) 1#(4(5(x1))) -> 2#(4(0(2(1(x1))))) 1#(4(5(x1))) -> 1#(2(4(0(2(1(x1)))))) 2#(5(1(x1))) -> 3#(x1) 2#(5(1(x1))) -> 2#(3(x1)) 2#(5(1(x1))) -> 1#(2(3(x1))) 2#(5(1(x1))) -> 2#(1(2(3(x1)))) 2#(5(1(x1))) -> 2#(2(1(2(3(x1))))) 2#(5(1(x1))) -> 2#(2(2(1(2(3(x1)))))) 2#(5(2(x1))) -> 3#(x1) 2#(5(2(x1))) -> 3#(3(x1)) 2#(5(2(x1))) -> 2#(3(3(x1))) 2#(5(2(x1))) -> 2#(2(3(3(x1)))) 2#(5(2(x1))) -> 4#(0(2(2(3(3(x1)))))) 2#(5(3(x1))) -> 3#(3(x1)) 2#(5(3(x1))) -> 1#(3(3(x1))) 2#(5(3(x1))) -> 4#(1(3(3(x1)))) 2#(5(3(x1))) -> 2#(0(4(1(3(3(x1)))))) 2#(5(4(x1))) -> 1#(x1) 2#(5(4(x1))) -> 1#(0(1(x1))) 2#(5(4(x1))) -> 5#(1(0(1(x1)))) 2#(5(4(x1))) -> 2#(0(5(1(0(1(x1)))))) 3#(2(5(x1))) -> 1#(0(5(x1))) 3#(2(5(x1))) -> 2#(0(1(0(5(x1))))) 3#(2(5(x1))) -> 3#(2(0(1(0(5(x1)))))) 3#(4(2(x1))) -> 2#(2(x1)) 3#(4(2(x1))) -> 2#(2(2(x1))) 3#(4(2(x1))) -> 4#(0(2(2(2(x1))))) 3#(4(2(x1))) -> 3#(4(0(2(2(2(x1)))))) 3#(5(1(x1))) -> 5#(x1) 3#(5(1(x1))) -> 2#(0(0(5(x1)))) 3#(5(1(x1))) -> 4#(2(0(0(5(x1))))) 3#(5(1(x1))) -> 4#(x1) 3#(5(1(x1))) -> 3#(4(x1)) 3#(5(1(x1))) -> 2#(3(4(x1))) 3#(5(1(x1))) -> 2#(2(3(4(x1)))) 3#(5(1(x1))) -> 4#(2(2(3(4(x1))))) 3#(5(1(x1))) -> 1#(0(1(x1))) 3#(5(1(x1))) -> 4#(1(0(1(x1)))) 3#(5(1(x1))) -> 1#(4(1(0(1(x1))))) 3#(5(1(x1))) -> 2#(1(4(1(0(1(x1)))))) 3#(5(2(x1))) -> 2#(2(x1)) 3#(5(2(x1))) -> 2#(2(2(x1))) 3#(5(2(x1))) -> 3#(2(2(2(x1)))) 3#(5(2(x1))) -> 4#(3(2(2(2(x1))))) 3#(5(2(x1))) -> 3#(0(x1)) 3#(5(2(x1))) -> 2#(3(0(x1))) 3#(5(2(x1))) -> 2#(2(3(0(x1)))) 3#(5(2(x1))) -> 2#(0(2(2(3(0(x1)))))) 3#(5(2(x1))) -> 1#(2(x1)) 3#(5(2(x1))) -> 2#(1(2(x1))) 3#(5(2(x1))) -> 3#(2(1(2(x1)))) 3#(5(2(x1))) -> 3#(3(2(1(2(x1))))) 3#(5(2(x1))) -> 2#(3(3(2(1(2(x1)))))) 3#(5(3(x1))) -> 3#(0(x1)) 3#(5(3(x1))) -> 3#(3(0(x1))) 3#(5(3(x1))) -> 4#(3(3(0(x1)))) 3#(5(3(x1))) -> 2#(4(3(3(0(x1))))) 3#(5(3(x1))) -> 5#(4(3(3(0(x1))))) 3#(5(3(x1))) -> 2#(x1) 3#(5(3(x1))) -> 4#(2(x1)) 3#(5(3(x1))) -> 4#(0(4(2(x1)))) 3#(5(3(x1))) -> 3#(4(0(4(2(x1))))) 3#(5(3(x1))) -> 2#(3(4(0(4(2(x1)))))) 3#(5(4(x1))) -> 5#(0(0(x1))) 3#(5(4(x1))) -> 2#(0(5(0(0(x1))))) 3#(5(4(x1))) -> 2#(x1) 3#(5(4(x1))) -> 1#(2(x1)) 3#(5(4(x1))) -> 5#(0(0(1(2(x1))))) 3#(5(5(x1))) -> 1#(0(5(x1))) 3#(5(5(x1))) -> 4#(1(0(5(x1)))) 3#(5(5(x1))) -> 5#(4(1(0(5(x1))))) 4#(5(1(x1))) -> 3#(x1) 4#(5(1(x1))) -> 3#(3(x1)) 4#(5(1(x1))) -> 5#(3(3(x1))) 4#(5(1(x1))) -> 1#(0(5(3(3(x1))))) 4#(5(1(x1))) -> 2#(1(0(5(3(3(x1)))))) 4#(5(2(x1))) -> 4#(x1) 4#(5(2(x1))) -> 1#(0(0(4(x1)))) 4#(5(2(x1))) -> 5#(1(0(0(4(x1))))) 4#(5(4(x1))) -> 2#(x1) 4#(5(4(x1))) -> 4#(2(x1)) 4#(5(4(x1))) -> 1#(0(4(2(x1)))) 4#(5(4(x1))) -> 2#(1(0(4(2(x1))))) 4#(5(4(x1))) -> 2#(2(1(0(4(2(x1)))))) 4#(5(4(x1))) -> 2#(0(x1)) 4#(5(4(x1))) -> 3#(2(0(x1))) 4#(5(4(x1))) -> 2#(0(3(2(0(x1))))) 4#(5(4(x1))) -> 3#(2(0(3(2(0(x1)))))) 5#(5(3(x1))) -> 2#(x1) 5#(5(3(x1))) -> 2#(2(x1)) 5#(5(3(x1))) -> 1#(2(2(x1))) 5#(5(3(x1))) -> 1#(0(1(2(2(x1))))) 5#(5(3(x1))) -> 5#(1(0(1(2(2(x1)))))) 5#(5(4(x1))) -> 2#(x1) 5#(5(4(x1))) -> 2#(2(x1)) 5#(5(4(x1))) -> 4#(2(2(x1))) 5#(5(4(x1))) -> 1#(0(4(2(2(x1))))) 5#(5(4(x1))) -> 5#(1(0(4(2(2(x1)))))) TRS: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) TDG Processor: DPs: 2#(5(x1)) -> 1#(0(x1)) 2#(5(x1)) -> 3#(0(1(0(x1)))) 2#(5(x1)) -> 3#(3(0(1(0(x1))))) 2#(5(x1)) -> 1#(3(3(0(1(0(x1)))))) 2#(5(x1)) -> 1#(x1) 2#(5(x1)) -> 5#(0(1(x1))) 2#(5(x1)) -> 2#(0(5(0(1(x1))))) 2#(5(x1)) -> 2#(2(0(5(0(1(x1)))))) 3#(5(x1)) -> 1#(x1) 3#(5(x1)) -> 2#(0(0(1(x1)))) 3#(5(x1)) -> 3#(2(0(0(1(x1))))) 3#(5(x1)) -> 1#(3(2(0(0(1(x1)))))) 3#(5(x1)) -> 3#(0(x1)) 3#(5(x1)) -> 5#(3(0(x1))) 3#(5(x1)) -> 2#(0(5(3(0(x1))))) 3#(5(x1)) -> 3#(2(0(5(3(0(x1)))))) 4#(5(x1)) -> 1#(x1) 4#(5(x1)) -> 2#(1(x1)) 4#(5(x1)) -> 3#(2(1(x1))) 4#(5(x1)) -> 1#(3(2(1(x1)))) 4#(5(x1)) -> 2#(1(3(2(1(x1))))) 4#(5(x1)) -> 2#(2(1(3(2(1(x1)))))) 4#(5(x1)) -> 5#(0(0(x1))) 4#(5(x1)) -> 2#(0(5(0(0(x1))))) 4#(5(x1)) -> 3#(2(0(5(0(0(x1)))))) 1#(2(5(x1))) -> 4#(x1) 1#(2(5(x1))) -> 5#(4(x1)) 1#(2(5(x1))) -> 5#(0(5(4(x1)))) 1#(2(5(x1))) -> 1#(0(5(0(5(4(x1)))))) 1#(2(5(x1))) -> 1#(x1) 1#(2(5(x1))) -> 1#(0(1(x1))) 1#(2(5(x1))) -> 2#(1(0(1(x1)))) 1#(2(5(x1))) -> 2#(2(1(0(1(x1))))) 1#(2(5(x1))) -> 1#(2(2(1(0(1(x1)))))) 1#(2(5(x1))) -> 1#(0(x1)) 1#(2(5(x1))) -> 3#(1(0(x1))) 1#(2(5(x1))) -> 1#(3(1(0(x1)))) 1#(2(5(x1))) -> 2#(0(1(3(1(0(x1)))))) 1#(4(5(x1))) -> 1#(x1) 1#(4(5(x1))) -> 2#(1(x1)) 1#(4(5(x1))) -> 4#(0(2(1(x1)))) 1#(4(5(x1))) -> 2#(4(0(2(1(x1))))) 1#(4(5(x1))) -> 1#(2(4(0(2(1(x1)))))) 2#(5(1(x1))) -> 3#(x1) 2#(5(1(x1))) -> 2#(3(x1)) 2#(5(1(x1))) -> 1#(2(3(x1))) 2#(5(1(x1))) -> 2#(1(2(3(x1)))) 2#(5(1(x1))) -> 2#(2(1(2(3(x1))))) 2#(5(1(x1))) -> 2#(2(2(1(2(3(x1)))))) 2#(5(2(x1))) -> 3#(x1) 2#(5(2(x1))) -> 3#(3(x1)) 2#(5(2(x1))) -> 2#(3(3(x1))) 2#(5(2(x1))) -> 2#(2(3(3(x1)))) 2#(5(2(x1))) -> 4#(0(2(2(3(3(x1)))))) 2#(5(3(x1))) -> 3#(3(x1)) 2#(5(3(x1))) -> 1#(3(3(x1))) 2#(5(3(x1))) -> 4#(1(3(3(x1)))) 2#(5(3(x1))) -> 2#(0(4(1(3(3(x1)))))) 2#(5(4(x1))) -> 1#(x1) 2#(5(4(x1))) -> 1#(0(1(x1))) 2#(5(4(x1))) -> 5#(1(0(1(x1)))) 2#(5(4(x1))) -> 2#(0(5(1(0(1(x1)))))) 3#(2(5(x1))) -> 1#(0(5(x1))) 3#(2(5(x1))) -> 2#(0(1(0(5(x1))))) 3#(2(5(x1))) -> 3#(2(0(1(0(5(x1)))))) 3#(4(2(x1))) -> 2#(2(x1)) 3#(4(2(x1))) -> 2#(2(2(x1))) 3#(4(2(x1))) -> 4#(0(2(2(2(x1))))) 3#(4(2(x1))) -> 3#(4(0(2(2(2(x1)))))) 3#(5(1(x1))) -> 5#(x1) 3#(5(1(x1))) -> 2#(0(0(5(x1)))) 3#(5(1(x1))) -> 4#(2(0(0(5(x1))))) 3#(5(1(x1))) -> 4#(x1) 3#(5(1(x1))) -> 3#(4(x1)) 3#(5(1(x1))) -> 2#(3(4(x1))) 3#(5(1(x1))) -> 2#(2(3(4(x1)))) 3#(5(1(x1))) -> 4#(2(2(3(4(x1))))) 3#(5(1(x1))) -> 1#(0(1(x1))) 3#(5(1(x1))) -> 4#(1(0(1(x1)))) 3#(5(1(x1))) -> 1#(4(1(0(1(x1))))) 3#(5(1(x1))) -> 2#(1(4(1(0(1(x1)))))) 3#(5(2(x1))) -> 2#(2(x1)) 3#(5(2(x1))) -> 2#(2(2(x1))) 3#(5(2(x1))) -> 3#(2(2(2(x1)))) 3#(5(2(x1))) -> 4#(3(2(2(2(x1))))) 3#(5(2(x1))) -> 3#(0(x1)) 3#(5(2(x1))) -> 2#(3(0(x1))) 3#(5(2(x1))) -> 2#(2(3(0(x1)))) 3#(5(2(x1))) -> 2#(0(2(2(3(0(x1)))))) 3#(5(2(x1))) -> 1#(2(x1)) 3#(5(2(x1))) -> 2#(1(2(x1))) 3#(5(2(x1))) -> 3#(2(1(2(x1)))) 3#(5(2(x1))) -> 3#(3(2(1(2(x1))))) 3#(5(2(x1))) -> 2#(3(3(2(1(2(x1)))))) 3#(5(3(x1))) -> 3#(0(x1)) 3#(5(3(x1))) -> 3#(3(0(x1))) 3#(5(3(x1))) -> 4#(3(3(0(x1)))) 3#(5(3(x1))) -> 2#(4(3(3(0(x1))))) 3#(5(3(x1))) -> 5#(4(3(3(0(x1))))) 3#(5(3(x1))) -> 2#(x1) 3#(5(3(x1))) -> 4#(2(x1)) 3#(5(3(x1))) -> 4#(0(4(2(x1)))) 3#(5(3(x1))) -> 3#(4(0(4(2(x1))))) 3#(5(3(x1))) -> 2#(3(4(0(4(2(x1)))))) 3#(5(4(x1))) -> 5#(0(0(x1))) 3#(5(4(x1))) -> 2#(0(5(0(0(x1))))) 3#(5(4(x1))) -> 2#(x1) 3#(5(4(x1))) -> 1#(2(x1)) 3#(5(4(x1))) -> 5#(0(0(1(2(x1))))) 3#(5(5(x1))) -> 1#(0(5(x1))) 3#(5(5(x1))) -> 4#(1(0(5(x1)))) 3#(5(5(x1))) -> 5#(4(1(0(5(x1))))) 4#(5(1(x1))) -> 3#(x1) 4#(5(1(x1))) -> 3#(3(x1)) 4#(5(1(x1))) -> 5#(3(3(x1))) 4#(5(1(x1))) -> 1#(0(5(3(3(x1))))) 4#(5(1(x1))) -> 2#(1(0(5(3(3(x1)))))) 4#(5(2(x1))) -> 4#(x1) 4#(5(2(x1))) -> 1#(0(0(4(x1)))) 4#(5(2(x1))) -> 5#(1(0(0(4(x1))))) 4#(5(4(x1))) -> 2#(x1) 4#(5(4(x1))) -> 4#(2(x1)) 4#(5(4(x1))) -> 1#(0(4(2(x1)))) 4#(5(4(x1))) -> 2#(1(0(4(2(x1))))) 4#(5(4(x1))) -> 2#(2(1(0(4(2(x1)))))) 4#(5(4(x1))) -> 2#(0(x1)) 4#(5(4(x1))) -> 3#(2(0(x1))) 4#(5(4(x1))) -> 2#(0(3(2(0(x1))))) 4#(5(4(x1))) -> 3#(2(0(3(2(0(x1)))))) 5#(5(3(x1))) -> 2#(x1) 5#(5(3(x1))) -> 2#(2(x1)) 5#(5(3(x1))) -> 1#(2(2(x1))) 5#(5(3(x1))) -> 1#(0(1(2(2(x1))))) 5#(5(3(x1))) -> 5#(1(0(1(2(2(x1)))))) 5#(5(4(x1))) -> 2#(x1) 5#(5(4(x1))) -> 2#(2(x1)) 5#(5(4(x1))) -> 4#(2(2(x1))) 5#(5(4(x1))) -> 1#(0(4(2(2(x1))))) 5#(5(4(x1))) -> 5#(1(0(4(2(2(x1)))))) TRS: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) graph: ... EDG Processor: DPs: 2#(5(x1)) -> 1#(0(x1)) 2#(5(x1)) -> 3#(0(1(0(x1)))) 2#(5(x1)) -> 3#(3(0(1(0(x1))))) 2#(5(x1)) -> 1#(3(3(0(1(0(x1)))))) 2#(5(x1)) -> 1#(x1) 2#(5(x1)) -> 5#(0(1(x1))) 2#(5(x1)) -> 2#(0(5(0(1(x1))))) 2#(5(x1)) -> 2#(2(0(5(0(1(x1)))))) 3#(5(x1)) -> 1#(x1) 3#(5(x1)) -> 2#(0(0(1(x1)))) 3#(5(x1)) -> 3#(2(0(0(1(x1))))) 3#(5(x1)) -> 1#(3(2(0(0(1(x1)))))) 3#(5(x1)) -> 3#(0(x1)) 3#(5(x1)) -> 5#(3(0(x1))) 3#(5(x1)) -> 2#(0(5(3(0(x1))))) 3#(5(x1)) -> 3#(2(0(5(3(0(x1)))))) 4#(5(x1)) -> 1#(x1) 4#(5(x1)) -> 2#(1(x1)) 4#(5(x1)) -> 3#(2(1(x1))) 4#(5(x1)) -> 1#(3(2(1(x1)))) 4#(5(x1)) -> 2#(1(3(2(1(x1))))) 4#(5(x1)) -> 2#(2(1(3(2(1(x1)))))) 4#(5(x1)) -> 5#(0(0(x1))) 4#(5(x1)) -> 2#(0(5(0(0(x1))))) 4#(5(x1)) -> 3#(2(0(5(0(0(x1)))))) 1#(2(5(x1))) -> 4#(x1) 1#(2(5(x1))) -> 5#(4(x1)) 1#(2(5(x1))) -> 5#(0(5(4(x1)))) 1#(2(5(x1))) -> 1#(0(5(0(5(4(x1)))))) 1#(2(5(x1))) -> 1#(x1) 1#(2(5(x1))) -> 1#(0(1(x1))) 1#(2(5(x1))) -> 2#(1(0(1(x1)))) 1#(2(5(x1))) -> 2#(2(1(0(1(x1))))) 1#(2(5(x1))) -> 1#(2(2(1(0(1(x1)))))) 1#(2(5(x1))) -> 1#(0(x1)) 1#(2(5(x1))) -> 3#(1(0(x1))) 1#(2(5(x1))) -> 1#(3(1(0(x1)))) 1#(2(5(x1))) -> 2#(0(1(3(1(0(x1)))))) 1#(4(5(x1))) -> 1#(x1) 1#(4(5(x1))) -> 2#(1(x1)) 1#(4(5(x1))) -> 4#(0(2(1(x1)))) 1#(4(5(x1))) -> 2#(4(0(2(1(x1))))) 1#(4(5(x1))) -> 1#(2(4(0(2(1(x1)))))) 2#(5(1(x1))) -> 3#(x1) 2#(5(1(x1))) -> 2#(3(x1)) 2#(5(1(x1))) -> 1#(2(3(x1))) 2#(5(1(x1))) -> 2#(1(2(3(x1)))) 2#(5(1(x1))) -> 2#(2(1(2(3(x1))))) 2#(5(1(x1))) -> 2#(2(2(1(2(3(x1)))))) 2#(5(2(x1))) -> 3#(x1) 2#(5(2(x1))) -> 3#(3(x1)) 2#(5(2(x1))) -> 2#(3(3(x1))) 2#(5(2(x1))) -> 2#(2(3(3(x1)))) 2#(5(2(x1))) -> 4#(0(2(2(3(3(x1)))))) 2#(5(3(x1))) -> 3#(3(x1)) 2#(5(3(x1))) -> 1#(3(3(x1))) 2#(5(3(x1))) -> 4#(1(3(3(x1)))) 2#(5(3(x1))) -> 2#(0(4(1(3(3(x1)))))) 2#(5(4(x1))) -> 1#(x1) 2#(5(4(x1))) -> 1#(0(1(x1))) 2#(5(4(x1))) -> 5#(1(0(1(x1)))) 2#(5(4(x1))) -> 2#(0(5(1(0(1(x1)))))) 3#(2(5(x1))) -> 1#(0(5(x1))) 3#(2(5(x1))) -> 2#(0(1(0(5(x1))))) 3#(2(5(x1))) -> 3#(2(0(1(0(5(x1)))))) 3#(4(2(x1))) -> 2#(2(x1)) 3#(4(2(x1))) -> 2#(2(2(x1))) 3#(4(2(x1))) -> 4#(0(2(2(2(x1))))) 3#(4(2(x1))) -> 3#(4(0(2(2(2(x1)))))) 3#(5(1(x1))) -> 5#(x1) 3#(5(1(x1))) -> 2#(0(0(5(x1)))) 3#(5(1(x1))) -> 4#(2(0(0(5(x1))))) 3#(5(1(x1))) -> 4#(x1) 3#(5(1(x1))) -> 3#(4(x1)) 3#(5(1(x1))) -> 2#(3(4(x1))) 3#(5(1(x1))) -> 2#(2(3(4(x1)))) 3#(5(1(x1))) -> 4#(2(2(3(4(x1))))) 3#(5(1(x1))) -> 1#(0(1(x1))) 3#(5(1(x1))) -> 4#(1(0(1(x1)))) 3#(5(1(x1))) -> 1#(4(1(0(1(x1))))) 3#(5(1(x1))) -> 2#(1(4(1(0(1(x1)))))) 3#(5(2(x1))) -> 2#(2(x1)) 3#(5(2(x1))) -> 2#(2(2(x1))) 3#(5(2(x1))) -> 3#(2(2(2(x1)))) 3#(5(2(x1))) -> 4#(3(2(2(2(x1))))) 3#(5(2(x1))) -> 3#(0(x1)) 3#(5(2(x1))) -> 2#(3(0(x1))) 3#(5(2(x1))) -> 2#(2(3(0(x1)))) 3#(5(2(x1))) -> 2#(0(2(2(3(0(x1)))))) 3#(5(2(x1))) -> 1#(2(x1)) 3#(5(2(x1))) -> 2#(1(2(x1))) 3#(5(2(x1))) -> 3#(2(1(2(x1)))) 3#(5(2(x1))) -> 3#(3(2(1(2(x1))))) 3#(5(2(x1))) -> 2#(3(3(2(1(2(x1)))))) 3#(5(3(x1))) -> 3#(0(x1)) 3#(5(3(x1))) -> 3#(3(0(x1))) 3#(5(3(x1))) -> 4#(3(3(0(x1)))) 3#(5(3(x1))) -> 2#(4(3(3(0(x1))))) 3#(5(3(x1))) -> 5#(4(3(3(0(x1))))) 3#(5(3(x1))) -> 2#(x1) 3#(5(3(x1))) -> 4#(2(x1)) 3#(5(3(x1))) -> 4#(0(4(2(x1)))) 3#(5(3(x1))) -> 3#(4(0(4(2(x1))))) 3#(5(3(x1))) -> 2#(3(4(0(4(2(x1)))))) 3#(5(4(x1))) -> 5#(0(0(x1))) 3#(5(4(x1))) -> 2#(0(5(0(0(x1))))) 3#(5(4(x1))) -> 2#(x1) 3#(5(4(x1))) -> 1#(2(x1)) 3#(5(4(x1))) -> 5#(0(0(1(2(x1))))) 3#(5(5(x1))) -> 1#(0(5(x1))) 3#(5(5(x1))) -> 4#(1(0(5(x1)))) 3#(5(5(x1))) -> 5#(4(1(0(5(x1))))) 4#(5(1(x1))) -> 3#(x1) 4#(5(1(x1))) -> 3#(3(x1)) 4#(5(1(x1))) -> 5#(3(3(x1))) 4#(5(1(x1))) -> 1#(0(5(3(3(x1))))) 4#(5(1(x1))) -> 2#(1(0(5(3(3(x1)))))) 4#(5(2(x1))) -> 4#(x1) 4#(5(2(x1))) -> 1#(0(0(4(x1)))) 4#(5(2(x1))) -> 5#(1(0(0(4(x1))))) 4#(5(4(x1))) -> 2#(x1) 4#(5(4(x1))) -> 4#(2(x1)) 4#(5(4(x1))) -> 1#(0(4(2(x1)))) 4#(5(4(x1))) -> 2#(1(0(4(2(x1))))) 4#(5(4(x1))) -> 2#(2(1(0(4(2(x1)))))) 4#(5(4(x1))) -> 2#(0(x1)) 4#(5(4(x1))) -> 3#(2(0(x1))) 4#(5(4(x1))) -> 2#(0(3(2(0(x1))))) 4#(5(4(x1))) -> 3#(2(0(3(2(0(x1)))))) 5#(5(3(x1))) -> 2#(x1) 5#(5(3(x1))) -> 2#(2(x1)) 5#(5(3(x1))) -> 1#(2(2(x1))) 5#(5(3(x1))) -> 1#(0(1(2(2(x1))))) 5#(5(3(x1))) -> 5#(1(0(1(2(2(x1)))))) 5#(5(4(x1))) -> 2#(x1) 5#(5(4(x1))) -> 2#(2(x1)) 5#(5(4(x1))) -> 4#(2(2(x1))) 5#(5(4(x1))) -> 1#(0(4(2(2(x1))))) 5#(5(4(x1))) -> 5#(1(0(4(2(2(x1)))))) TRS: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) graph: ... SCC Processor: #sccs: 1 #rules: 60 #arcs: 1793/19321 DPs: 4#(5(4(x1))) -> 4#(2(x1)) 4#(5(4(x1))) -> 2#(x1) 2#(5(4(x1))) -> 1#(x1) 1#(4(5(x1))) -> 2#(1(x1)) 2#(5(3(x1))) -> 4#(1(3(3(x1)))) 4#(5(2(x1))) -> 4#(x1) 4#(5(1(x1))) -> 5#(3(3(x1))) 5#(5(4(x1))) -> 4#(2(2(x1))) 4#(5(1(x1))) -> 3#(3(x1)) 3#(5(4(x1))) -> 1#(2(x1)) 1#(4(5(x1))) -> 1#(x1) 1#(2(5(x1))) -> 1#(x1) 1#(2(5(x1))) -> 5#(4(x1)) 5#(5(4(x1))) -> 2#(2(x1)) 2#(5(3(x1))) -> 1#(3(3(x1))) 1#(2(5(x1))) -> 4#(x1) 4#(5(1(x1))) -> 3#(x1) 3#(5(4(x1))) -> 2#(x1) 2#(5(3(x1))) -> 3#(3(x1)) 3#(5(3(x1))) -> 4#(2(x1)) 4#(5(x1)) -> 2#(2(1(3(2(1(x1)))))) 2#(5(2(x1))) -> 2#(2(3(3(x1)))) 2#(5(2(x1))) -> 2#(3(3(x1))) 2#(5(2(x1))) -> 3#(3(x1)) 3#(5(3(x1))) -> 2#(x1) 2#(5(2(x1))) -> 3#(x1) 3#(5(2(x1))) -> 2#(3(3(2(1(2(x1)))))) 2#(5(1(x1))) -> 2#(2(2(1(2(3(x1)))))) 2#(5(1(x1))) -> 2#(2(1(2(3(x1))))) 2#(5(1(x1))) -> 2#(1(2(3(x1)))) 2#(5(1(x1))) -> 1#(2(3(x1))) 2#(5(1(x1))) -> 2#(3(x1)) 2#(5(1(x1))) -> 3#(x1) 3#(5(2(x1))) -> 3#(3(2(1(2(x1))))) 3#(5(2(x1))) -> 3#(2(1(2(x1)))) 3#(5(2(x1))) -> 2#(1(2(x1))) 2#(5(x1)) -> 1#(x1) 3#(5(2(x1))) -> 1#(2(x1)) 3#(5(2(x1))) -> 4#(3(2(2(2(x1))))) 4#(5(x1)) -> 2#(1(3(2(1(x1))))) 4#(5(x1)) -> 1#(3(2(1(x1)))) 4#(5(x1)) -> 3#(2(1(x1))) 3#(5(2(x1))) -> 3#(2(2(2(x1)))) 3#(5(2(x1))) -> 2#(2(2(x1))) 3#(5(2(x1))) -> 2#(2(x1)) 3#(5(1(x1))) -> 4#(2(2(3(4(x1))))) 4#(5(x1)) -> 2#(1(x1)) 4#(5(x1)) -> 1#(x1) 3#(5(1(x1))) -> 2#(2(3(4(x1)))) 3#(5(1(x1))) -> 2#(3(4(x1))) 3#(5(1(x1))) -> 3#(4(x1)) 3#(5(1(x1))) -> 4#(x1) 3#(5(1(x1))) -> 5#(x1) 5#(5(4(x1))) -> 2#(x1) 5#(5(3(x1))) -> 1#(2(2(x1))) 5#(5(3(x1))) -> 2#(2(x1)) 5#(5(3(x1))) -> 2#(x1) 3#(4(2(x1))) -> 2#(2(2(x1))) 3#(4(2(x1))) -> 2#(2(x1)) 3#(5(x1)) -> 1#(x1) TRS: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) KBO Processor: argument filtering: pi(5) = [0] pi(2) = [0] pi(0) = [] pi(1) = 0 pi(3) = 0 pi(4) = 0 pi(2#) = [0] pi(1#) = 0 pi(3#) = [0] pi(5#) = 0 pi(4#) = [0] weight function: w0 = 1 w(3#) = w(1#) = w(0) = w(5) = 1 w(4#) = w(5#) = w(2#) = w(4) = w(3) = w(1) = w(2) = 0 precedence: 4# ~ 2# ~ 2 > 5# ~ 3# ~ 1# ~ 4 ~ 3 ~ 1 ~ 0 ~ 5 problem: DPs: TRS: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) Qed