YES Problem: 0(0(1(2(x1)))) -> 2(3(0(x1))) 4(2(5(2(x1)))) -> 1(4(0(x1))) 4(5(3(4(x1)))) -> 4(4(2(4(x1)))) 1(3(5(5(2(x1))))) -> 1(3(2(3(x1)))) 5(2(2(1(2(x1))))) -> 0(0(2(3(x1)))) 2(2(5(3(2(2(x1)))))) -> 5(1(1(0(3(x1))))) 2(5(1(2(1(1(x1)))))) -> 5(2(1(2(4(1(x1)))))) 3(4(1(4(2(4(x1)))))) -> 1(3(3(3(x1)))) 3(5(2(2(4(5(x1)))))) -> 3(2(4(3(0(x1))))) 5(2(1(0(1(5(x1)))))) -> 5(4(2(4(5(1(x1)))))) 1(3(5(4(1(2(2(x1))))))) -> 3(3(3(4(4(0(x1)))))) 4(5(4(3(0(5(1(x1))))))) -> 4(3(3(5(4(1(x1)))))) 2(1(5(2(1(3(4(4(x1)))))))) -> 4(0(3(4(0(1(2(x1))))))) 5(4(0(2(2(4(0(4(x1)))))))) -> 3(1(5(1(3(0(4(x1))))))) 3(4(2(1(1(2(2(5(4(x1))))))))) -> 3(3(3(1(3(3(4(x1))))))) 5(4(4(5(0(1(4(5(4(x1))))))))) -> 1(5(5(0(4(1(4(5(4(x1))))))))) 5(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5(3(4(5(0(1(4(0(3(x1))))))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1))))))))))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1)))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1))))))))))))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1))))))))))))))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1)))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1)))))))))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1)))))))))))))))))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))))))))))) Proof: DP Processor: DPs: 0#(0(1(2(x1)))) -> 0#(x1) 0#(0(1(2(x1)))) -> 3#(0(x1)) 0#(0(1(2(x1)))) -> 2#(3(0(x1))) 4#(2(5(2(x1)))) -> 0#(x1) 4#(2(5(2(x1)))) -> 4#(0(x1)) 4#(2(5(2(x1)))) -> 1#(4(0(x1))) 4#(5(3(4(x1)))) -> 2#(4(x1)) 4#(5(3(4(x1)))) -> 4#(2(4(x1))) 4#(5(3(4(x1)))) -> 4#(4(2(4(x1)))) 1#(3(5(5(2(x1))))) -> 3#(x1) 1#(3(5(5(2(x1))))) -> 2#(3(x1)) 1#(3(5(5(2(x1))))) -> 3#(2(3(x1))) 1#(3(5(5(2(x1))))) -> 1#(3(2(3(x1)))) 5#(2(2(1(2(x1))))) -> 3#(x1) 5#(2(2(1(2(x1))))) -> 2#(3(x1)) 5#(2(2(1(2(x1))))) -> 0#(2(3(x1))) 5#(2(2(1(2(x1))))) -> 0#(0(2(3(x1)))) 2#(2(5(3(2(2(x1)))))) -> 3#(x1) 2#(2(5(3(2(2(x1)))))) -> 0#(3(x1)) 2#(2(5(3(2(2(x1)))))) -> 1#(0(3(x1))) 2#(2(5(3(2(2(x1)))))) -> 1#(1(0(3(x1)))) 2#(2(5(3(2(2(x1)))))) -> 5#(1(1(0(3(x1))))) 2#(5(1(2(1(1(x1)))))) -> 4#(1(x1)) 2#(5(1(2(1(1(x1)))))) -> 2#(4(1(x1))) 2#(5(1(2(1(1(x1)))))) -> 1#(2(4(1(x1)))) 2#(5(1(2(1(1(x1)))))) -> 2#(1(2(4(1(x1))))) 2#(5(1(2(1(1(x1)))))) -> 5#(2(1(2(4(1(x1)))))) 3#(4(1(4(2(4(x1)))))) -> 3#(x1) 3#(4(1(4(2(4(x1)))))) -> 3#(3(x1)) 3#(4(1(4(2(4(x1)))))) -> 3#(3(3(x1))) 3#(4(1(4(2(4(x1)))))) -> 1#(3(3(3(x1)))) 3#(5(2(2(4(5(x1)))))) -> 0#(x1) 3#(5(2(2(4(5(x1)))))) -> 3#(0(x1)) 3#(5(2(2(4(5(x1)))))) -> 4#(3(0(x1))) 3#(5(2(2(4(5(x1)))))) -> 2#(4(3(0(x1)))) 3#(5(2(2(4(5(x1)))))) -> 3#(2(4(3(0(x1))))) 5#(2(1(0(1(5(x1)))))) -> 1#(x1) 5#(2(1(0(1(5(x1)))))) -> 5#(1(x1)) 5#(2(1(0(1(5(x1)))))) -> 4#(5(1(x1))) 5#(2(1(0(1(5(x1)))))) -> 2#(4(5(1(x1)))) 5#(2(1(0(1(5(x1)))))) -> 4#(2(4(5(1(x1))))) 5#(2(1(0(1(5(x1)))))) -> 5#(4(2(4(5(1(x1)))))) 1#(3(5(4(1(2(2(x1))))))) -> 0#(x1) 1#(3(5(4(1(2(2(x1))))))) -> 4#(0(x1)) 1#(3(5(4(1(2(2(x1))))))) -> 4#(4(0(x1))) 1#(3(5(4(1(2(2(x1))))))) -> 3#(4(4(0(x1)))) 1#(3(5(4(1(2(2(x1))))))) -> 3#(3(4(4(0(x1))))) 1#(3(5(4(1(2(2(x1))))))) -> 3#(3(3(4(4(0(x1)))))) 4#(5(4(3(0(5(1(x1))))))) -> 4#(1(x1)) 4#(5(4(3(0(5(1(x1))))))) -> 5#(4(1(x1))) 4#(5(4(3(0(5(1(x1))))))) -> 3#(5(4(1(x1)))) 4#(5(4(3(0(5(1(x1))))))) -> 3#(3(5(4(1(x1))))) 4#(5(4(3(0(5(1(x1))))))) -> 4#(3(3(5(4(1(x1)))))) 2#(1(5(2(1(3(4(4(x1)))))))) -> 2#(x1) 2#(1(5(2(1(3(4(4(x1)))))))) -> 1#(2(x1)) 2#(1(5(2(1(3(4(4(x1)))))))) -> 0#(1(2(x1))) 2#(1(5(2(1(3(4(4(x1)))))))) -> 4#(0(1(2(x1)))) 2#(1(5(2(1(3(4(4(x1)))))))) -> 3#(4(0(1(2(x1))))) 2#(1(5(2(1(3(4(4(x1)))))))) -> 0#(3(4(0(1(2(x1)))))) 2#(1(5(2(1(3(4(4(x1)))))))) -> 4#(0(3(4(0(1(2(x1))))))) 5#(4(0(2(2(4(0(4(x1)))))))) -> 3#(0(4(x1))) 5#(4(0(2(2(4(0(4(x1)))))))) -> 1#(3(0(4(x1)))) 5#(4(0(2(2(4(0(4(x1)))))))) -> 5#(1(3(0(4(x1))))) 5#(4(0(2(2(4(0(4(x1)))))))) -> 1#(5(1(3(0(4(x1)))))) 5#(4(0(2(2(4(0(4(x1)))))))) -> 3#(1(5(1(3(0(4(x1))))))) 3#(4(2(1(1(2(2(5(4(x1))))))))) -> 3#(4(x1)) 3#(4(2(1(1(2(2(5(4(x1))))))))) -> 3#(3(4(x1))) 3#(4(2(1(1(2(2(5(4(x1))))))))) -> 1#(3(3(4(x1)))) 3#(4(2(1(1(2(2(5(4(x1))))))))) -> 3#(1(3(3(4(x1))))) 3#(4(2(1(1(2(2(5(4(x1))))))))) -> 3#(3(1(3(3(4(x1)))))) 3#(4(2(1(1(2(2(5(4(x1))))))))) -> 3#(3(3(1(3(3(4(x1))))))) 5#(4(4(5(0(1(4(5(4(x1))))))))) -> 4#(1(4(5(4(x1))))) 5#(4(4(5(0(1(4(5(4(x1))))))))) -> 0#(4(1(4(5(4(x1)))))) 5#(4(4(5(0(1(4(5(4(x1))))))))) -> 5#(0(4(1(4(5(4(x1))))))) 5#(4(4(5(0(1(4(5(4(x1))))))))) -> 5#(5(0(4(1(4(5(4(x1)))))))) 5#(4(4(5(0(1(4(5(4(x1))))))))) -> 1#(5(5(0(4(1(4(5(4(x1))))))))) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 3#(x1) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 0#(3(x1)) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 4#(0(3(x1))) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 1#(4(0(3(x1)))) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 0#(1(4(0(3(x1))))) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5#(0(1(4(0(3(x1)))))) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 4#(5(0(1(4(0(3(x1))))))) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 3#(4(5(0(1(4(0(3(x1)))))))) 5#(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 0#(x1) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 2#(0(x1)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 4#(2(0(x1))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 3#(4(2(0(x1)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 4#(3(4(2(0(x1))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 3#(4(3(4(2(0(x1)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 2#(3(4(3(4(2(0(x1))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 4#(2(3(4(3(4(2(0(x1)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 2#(0(x1)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 0#(2(0(x1))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 0#(0(2(0(x1)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 0#(0(0(2(0(x1))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 4#(0(0(0(2(0(x1)))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 0#(4(0(0(0(2(0(x1))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 3#(0(4(0(0(0(2(0(x1)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 0#(x1) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 3#(0(x1)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 3#(3(0(x1))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 1#(3(3(0(x1)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 5#(1(3(3(0(x1))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 0#(5(1(3(3(0(x1)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 3#(0(5(1(3(3(0(x1))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 0#(x1) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 0#(0(x1)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 4#(0(0(x1))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 5#(4(0(0(x1)))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 4#(5(4(0(0(x1))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 0#(4(5(4(0(0(x1)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 0#(0(4(5(4(0(0(x1))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1))))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 4#(1(x1)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 0#(4(1(x1))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 5#(0(4(1(x1)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 3#(5(0(4(1(x1))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 3#(3(5(0(4(1(x1)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 0#(3(3(5(0(4(1(x1))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1)))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1)))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 3#(x1) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 1#(3(x1)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 2#(1(3(x1))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 2#(2(1(3(x1)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 3#(2(2(1(3(x1))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 0#(3(2(2(1(3(x1)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 1#(0(3(2(2(1(3(x1))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 3#(3(1(x1))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 4#(3(3(1(x1)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 1#(4(3(3(1(x1))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 5#(1(4(3(3(1(x1)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 1#(x1) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 3#(1(x1)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 4#(3(1(x1))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 3#(4(3(1(x1)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 2#(3(4(3(1(x1))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 1#(2(3(4(3(1(x1)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))))))))))) TRS: 0(0(1(2(x1)))) -> 2(3(0(x1))) 4(2(5(2(x1)))) -> 1(4(0(x1))) 4(5(3(4(x1)))) -> 4(4(2(4(x1)))) 1(3(5(5(2(x1))))) -> 1(3(2(3(x1)))) 5(2(2(1(2(x1))))) -> 0(0(2(3(x1)))) 2(2(5(3(2(2(x1)))))) -> 5(1(1(0(3(x1))))) 2(5(1(2(1(1(x1)))))) -> 5(2(1(2(4(1(x1)))))) 3(4(1(4(2(4(x1)))))) -> 1(3(3(3(x1)))) 3(5(2(2(4(5(x1)))))) -> 3(2(4(3(0(x1))))) 5(2(1(0(1(5(x1)))))) -> 5(4(2(4(5(1(x1)))))) 1(3(5(4(1(2(2(x1))))))) -> 3(3(3(4(4(0(x1)))))) 4(5(4(3(0(5(1(x1))))))) -> 4(3(3(5(4(1(x1)))))) 2(1(5(2(1(3(4(4(x1)))))))) -> 4(0(3(4(0(1(2(x1))))))) 5(4(0(2(2(4(0(4(x1)))))))) -> 3(1(5(1(3(0(4(x1))))))) 3(4(2(1(1(2(2(5(4(x1))))))))) -> 3(3(3(1(3(3(4(x1))))))) 5(4(4(5(0(1(4(5(4(x1))))))))) -> 1(5(5(0(4(1(4(5(4(x1))))))))) 5(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5(3(4(5(0(1(4(0(3(x1))))))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1))))))))))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1)))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1))))))))))))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1))))))))))))))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1)))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1)))))))))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1)))))))))))))))))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))))))))))) KBO Processor: weight function: w0 = 1 w(5#) = w(1#) = w(4#) = w(2#) = w(3#) = w(4) = w(5) = w(3) = w(0) = w( 1) = w(2) = 1 w(0#) = 0 precedence: 0# > 2# ~ 2 > 5# ~ 5 ~ 0 > 1# ~ 4# ~ 3# ~ 4 ~ 3 ~ 1 problem: DPs: TRS: Qed