2.69/1.29 YES 2.92/1.30 2.92/1.30 Problem: 2.92/1.30 0(1(0(1(x1)))) -> 0(2(3(1(x1)))) 2.92/1.30 2(1(4(0(1(x1))))) -> 3(0(0(1(x1)))) 2.92/1.30 2(3(3(3(1(x1))))) -> 1(1(3(1(x1)))) 2.92/1.30 4(1(2(3(4(x1))))) -> 1(5(3(0(x1)))) 2.92/1.30 5(3(2(4(4(x1))))) -> 0(1(3(0(x1)))) 2.92/1.30 5(5(0(4(3(3(x1)))))) -> 0(3(2(1(3(x1))))) 2.92/1.30 5(0(3(1(4(1(0(1(0(x1))))))))) -> 2(2(4(1(3(2(2(3(0(x1))))))))) 2.92/1.30 5(5(5(4(4(0(4(0(2(1(x1)))))))))) -> 5(4(5(4(0(5(0(4(0(3(x1)))))))))) 2.92/1.30 2(2(2(0(3(3(2(0(4(5(0(x1))))))))))) -> 0(4(0(0(0(0(2(5(1(x1))))))))) 2.92/1.30 1(0(2(0(3(5(1(4(5(2(4(4(x1)))))))))))) -> 1(0(1(0(3(2(3(2(1(0(3(3(x1)))))))))))) 2.92/1.30 4(0(4(2(3(5(0(1(4(4(5(0(x1)))))))))))) -> 3(5(0(2(5(1(2(5(1(4(1(x1))))))))))) 2.92/1.30 4(1(0(2(3(5(4(1(4(4(1(1(x1)))))))))))) -> 2(5(4(4(5(5(1(2(4(4(2(x1))))))))))) 2.92/1.30 2(0(0(5(5(0(2(2(2(3(4(1(4(x1))))))))))))) -> 3(3(3(3(1(3(1(4(1(4(5(4(3(x1))))))))))))) 2.92/1.30 4(5(1(3(0(0(3(5(2(1(2(5(2(x1))))))))))))) -> 4(5(0(3(5(3(5(5(3(5(4(0(4(x1))))))))))))) 2.92/1.30 2(1(4(5(5(0(2(4(0(5(4(4(1(4(x1)))))))))))))) -> 0(0(2(1(4(3(2(5(3(2(5(2(1(x1))))))))))))) 2.92/1.30 3(1(3(5(4(1(1(4(5(1(1(3(5(1(x1)))))))))))))) -> 3(2(1(2(4(3(5(1(5(5(1(3(4(x1))))))))))))) 2.92/1.30 4(4(5(3(0(2(0(0(0(3(5(0(2(1(x1)))))))))))))) -> 2(2(0(4(1(0(0(1(4(2(4(1(3(5(x1)))))))))))))) 2.92/1.30 5(0(5(4(4(4(4(2(5(1(2(3(3(1(1(x1))))))))))))))) -> 1(3(0(5(3(1(3(1(0(3(3(1(0(3(x1)))))))))))))) 2.92/1.30 5(3(5(5(4(0(2(2(4(3(2(2(1(4(1(x1))))))))))))))) -> 5(1(4(2(3(5(4(0(4(4(2(1(0(0(x1)))))))))))))) 2.92/1.30 5(5(2(1(3(3(2(5(0(1(0(5(0(5(0(x1))))))))))))))) -> 2(3(5(0(2(4(1(0(5(4(3(0(5(0(x1)))))))))))))) 2.92/1.30 2(1(2(3(2(1(2(5(5(5(0(0(3(2(1(1(x1)))))))))))))))) -> 2.92/1.30 4(4(1(1(3(3(1(4(2(1(3(0(3(2(3(x1))))))))))))))) 2.92/1.30 3(3(3(1(4(2(0(0(3(0(1(1(3(4(1(2(x1)))))))))))))))) -> 2.92/1.30 3(0(4(1(5(0(5(3(5(0(4(4(3(0(4(x1))))))))))))))) 2.92/1.30 2(1(1(3(5(4(0(1(4(2(5(1(4(5(4(5(1(x1))))))))))))))))) -> 2.92/1.30 2(3(3(3(3(2(1(4(5(5(2(2(4(4(4(3(0(x1))))))))))))))))) 2.92/1.30 5(0(2(4(4(4(4(3(1(2(2(2(2(2(2(5(2(x1))))))))))))))))) -> 2.92/1.30 5(4(0(4(4(3(5(5(4(3(0(5(5(5(0(0(x1)))))))))))))))) 2.92/1.30 2(5(5(1(0(4(4(1(4(0(5(1(1(5(0(0(1(4(x1)))))))))))))))))) -> 2.92/1.30 3(3(1(0(0(1(1(1(2(1(2(0(2(4(4(3(5(0(x1)))))))))))))))))) 2.92/1.30 0(0(1(1(4(5(3(2(5(3(4(4(3(0(5(4(4(4(2(x1))))))))))))))))))) -> 2.92/1.30 0(0(4(5(1(4(1(5(3(0(4(0(3(3(4(0(4(0(4(x1))))))))))))))))))) 2.92/1.30 1(4(1(4(1(5(2(4(4(3(3(4(5(4(4(1(2(0(2(3(x1)))))))))))))))))))) -> 2.92/1.30 1(2(1(5(0(1(0(4(4(4(2(5(0(1(5(1(1(4(3(3(x1)))))))))))))))))))) 2.92/1.30 2(1(0(0(4(2(5(5(1(3(3(4(3(3(5(5(3(3(5(2(x1)))))))))))))))))))) -> 2.92/1.30 4(4(3(3(5(0(4(2(2(1(1(3(1(5(2(5(2(4(5(x1))))))))))))))))))) 2.92/1.30 4(2(4(2(4(5(4(5(2(1(5(3(1(0(2(5(2(1(4(2(4(x1))))))))))))))))))))) -> 2.92/1.30 1(5(3(1(5(0(5(2(0(5(4(3(5(2(1(2(5(4(3(2(1(x1))))))))))))))))))))) 2.92/1.30 5(0(2(1(0(3(4(3(4(1(5(3(3(3(4(2(0(5(5(3(5(x1))))))))))))))))))))) -> 2.92/1.30 3(5(1(1(0(5(4(5(2(1(5(0(4(4(4(3(4(4(1(5(x1)))))))))))))))))))) 2.92/1.30 2.92/1.30 Proof: 2.92/1.30 String Reversal Processor: 2.92/1.30 1(0(1(0(x1)))) -> 1(3(2(0(x1)))) 2.92/1.30 1(0(4(1(2(x1))))) -> 1(0(0(3(x1)))) 2.92/1.30 1(3(3(3(2(x1))))) -> 1(3(1(1(x1)))) 2.92/1.30 4(3(2(1(4(x1))))) -> 0(3(5(1(x1)))) 2.92/1.30 4(4(2(3(5(x1))))) -> 0(3(1(0(x1)))) 2.92/1.30 3(3(4(0(5(5(x1)))))) -> 3(1(2(3(0(x1))))) 2.92/1.30 0(1(0(1(4(1(3(0(5(x1))))))))) -> 0(3(2(2(3(1(4(2(2(x1))))))))) 2.92/1.30 1(2(0(4(0(4(4(5(5(5(x1)))))))))) -> 3(0(4(0(5(0(4(5(4(5(x1)))))))))) 2.92/1.30 0(5(4(0(2(3(3(0(2(2(2(x1))))))))))) -> 1(5(2(0(0(0(0(4(0(x1))))))))) 2.92/1.30 4(4(2(5(4(1(5(3(0(2(0(1(x1)))))))))))) -> 3(3(0(1(2(3(2(3(0(1(0(1(x1)))))))))))) 2.92/1.30 0(5(4(4(1(0(5(3(2(4(0(4(x1)))))))))))) -> 1(4(1(5(2(1(5(2(0(5(3(x1))))))))))) 2.92/1.30 1(1(4(4(1(4(5(3(2(0(1(4(x1)))))))))))) -> 2(4(4(2(1(5(5(4(4(5(2(x1))))))))))) 2.92/1.30 4(1(4(3(2(2(2(0(5(5(0(0(2(x1))))))))))))) -> 3(4(5(4(1(4(1(3(1(3(3(3(3(x1))))))))))))) 2.92/1.30 2(5(2(1(2(5(3(0(0(3(1(5(4(x1))))))))))))) -> 4(0(4(5(3(5(5(3(5(3(0(5(4(x1))))))))))))) 2.92/1.30 4(1(4(4(5(0(4(2(0(5(5(4(1(2(x1)))))))))))))) -> 1(2(5(2(3(5(2(3(4(1(2(0(0(x1))))))))))))) 2.92/1.30 1(5(3(1(1(5(4(1(1(4(5(3(1(3(x1)))))))))))))) -> 4(3(1(5(5(1(5(3(4(2(1(2(3(x1))))))))))))) 2.92/1.30 1(2(0(5(3(0(0(0(2(0(3(5(4(4(x1)))))))))))))) -> 5(3(1(4(2(4(1(0(0(1(4(0(2(2(x1)))))))))))))) 2.92/1.30 1(1(3(3(2(1(5(2(4(4(4(4(5(0(5(x1))))))))))))))) -> 3(0(1(3(3(0(1(3(1(3(5(0(3(1(x1)))))))))))))) 2.92/1.30 1(4(1(2(2(3(4(2(2(0(4(5(5(3(5(x1))))))))))))))) -> 0(0(1(2(4(4(0(4(5(3(2(4(1(5(x1)))))))))))))) 2.92/1.30 0(5(0(5(0(1(0(5(2(3(3(1(2(5(5(x1))))))))))))))) -> 0(5(0(3(4(5(0(1(4(2(0(5(3(2(x1)))))))))))))) 2.92/1.30 1(1(2(3(0(0(5(5(5(2(1(2(3(2(1(2(x1)))))))))))))))) -> 2.92/1.31 3(2(3(0(3(1(2(4(1(3(3(1(1(4(4(x1))))))))))))))) 2.92/1.31 2(1(4(3(1(1(0(3(0(0(2(4(1(3(3(3(x1)))))))))))))))) -> 2.92/1.31 4(0(3(4(4(0(5(3(5(0(5(1(4(0(3(x1))))))))))))))) 2.92/1.31 1(5(4(5(4(1(5(2(4(1(0(4(5(3(1(1(2(x1))))))))))))))))) -> 2.92/1.31 0(3(4(4(4(2(2(5(5(4(1(2(3(3(3(3(2(x1))))))))))))))))) 2.92/1.31 2(5(2(2(2(2(2(2(1(3(4(4(4(4(2(0(5(x1))))))))))))))))) -> 2.92/1.31 0(0(5(5(5(0(3(4(5(5(3(4(4(0(4(5(x1)))))))))))))))) 2.92/1.31 4(1(0(0(5(1(1(5(0(4(1(4(4(0(1(5(5(2(x1)))))))))))))))))) -> 2.92/1.31 0(5(3(4(4(2(0(2(1(2(1(1(1(0(0(1(3(3(x1)))))))))))))))))) 2.92/1.31 2(4(4(4(5(0(3(4(4(3(5(2(3(5(4(1(1(0(0(x1))))))))))))))))))) -> 2.92/1.31 4(0(4(0(4(3(3(0(4(0(3(5(1(4(1(5(4(0(0(x1))))))))))))))))))) 2.92/1.31 3(2(0(2(1(4(4(5(4(3(3(4(4(2(5(1(4(1(4(1(x1)))))))))))))))))))) -> 2.92/1.31 3(3(4(1(1(5(1(0(5(2(4(4(4(0(1(0(5(1(2(1(x1)))))))))))))))))))) 2.92/1.31 2(5(3(3(5(5(3(3(4(3(3(1(5(5(2(4(0(0(1(2(x1)))))))))))))))))))) -> 2.92/1.31 5(4(2(5(2(5(1(3(1(1(2(2(4(0(5(3(3(4(4(x1))))))))))))))))))) 2.92/1.31 4(2(4(1(2(5(2(0(1(3(5(1(2(5(4(5(4(2(4(2(4(x1))))))))))))))))))))) -> 2.92/1.31 1(2(3(4(5(2(1(2(5(3(4(5(0(2(5(0(5(1(3(5(1(x1))))))))))))))))))))) 2.92/1.31 5(3(5(5(0(2(4(3(3(3(5(1(4(3(4(3(0(1(2(0(5(x1))))))))))))))))))))) -> 2.92/1.31 5(1(4(4(3(4(4(4(0(5(1(2(5(4(5(0(1(1(5(3(x1)))))))))))))))))))) 2.92/1.31 KBO Processor: 2.92/1.31 weight function: 2.92/1.31 w0 = 1 2.92/1.31 w(5) = w(4) = w(2) = w(3) = w(0) = w(1) = 1 2.92/1.31 precedence: 2.92/1.31 2 > 4 > 1 > 0 > 5 ~ 3 2.92/1.31 problem: 2.92/1.31 2.92/1.31 Qed 2.92/1.31 EOF