/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: sq(0(x1)) -> p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(x1))))))))))))))))) sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) 0(x1) -> x1 Proof: String Reversal Processor: 0(sq(x1)) -> s(p(s(p(0(s(s(s(s(p(p(p(p(s(p(s(p(x1))))))))))))))))) s(sq(x1)) -> s(s(s(s(s(s(p(p(p(p(p(p(sq(s(s(s(p(p(p(s(p(s(p(twice(s(s(p(p(s(p(s(p(s(x1))))))))))))))))))))))))))))))))) 0(twice(x1)) -> s(p(s(p(s(p(s(s(p(p(s(s(s(p(p(p(0(s(s(s(p(s(s(p(p(p(p(x1))))))))))))))))))))))))))) s(twice(x1)) -> s(p(s(p(twice(s(s(s(p(p(s(s(s(p(p(x1))))))))))))))) s(p(p(x1))) -> p(x1) s(p(x1)) -> x1 0(p(x1)) -> s(s(s(s(s(s(s(s(s(s(s(0(x1)))))))))))) 0(x1) -> x1 Matrix Interpretation Processor: dim=1 interpretation: [twice](x0) = x0, [p](x0) = x0, [s](x0) = x0, [sq](x0) = x0, [0](x0) = x0 + 7 orientation: 0(sq(x1)) = x1 + 7 >= x1 + 7 = s(p(s(p(0(s(s(s(s(p(p(p(p(s(p(s(p(x1))))))))))))))))) s(sq(x1)) = x1 >= x1 = s(s(s(s(s(s(p(p(p(p(p(p(sq(s(s(s(p(p(p(s(p(s(p(twice(s(s(p(p(s(p(s(p(s(x1))))))))))))))))))))))))))))))))) 0(twice(x1)) = x1 + 7 >= x1 + 7 = s(p(s(p(s(p(s(s(p(p(s(s(s(p(p(p(0(s(s(s(p(s(s(p(p(p(p(x1))))))))))))))))))))))))))) s(twice(x1)) = x1 >= x1 = s(p(s(p(twice(s(s(s(p(p(s(s(s(p(p(x1))))))))))))))) s(p(p(x1))) = x1 >= x1 = p(x1) s(p(x1)) = x1 >= x1 = x1 0(p(x1)) = x1 + 7 >= x1 + 7 = s(s(s(s(s(s(s(s(s(s(s(0(x1)))))))))))) 0(x1) = x1 + 7 >= x1 = x1 problem: 0(sq(x1)) -> s(p(s(p(0(s(s(s(s(p(p(p(p(s(p(s(p(x1))))))))))))))))) s(sq(x1)) -> s(s(s(s(s(s(p(p(p(p(p(p(sq(s(s(s(p(p(p(s(p(s(p(twice(s(s(p(p(s(p(s(p(s(x1))))))))))))))))))))))))))))))))) 0(twice(x1)) -> s(p(s(p(s(p(s(s(p(p(s(s(s(p(p(p(0(s(s(s(p(s(s(p(p(p(p(x1))))))))))))))))))))))))))) s(twice(x1)) -> s(p(s(p(twice(s(s(s(p(p(s(s(s(p(p(x1))))))))))))))) s(p(p(x1))) -> p(x1) s(p(x1)) -> x1 0(p(x1)) -> s(s(s(s(s(s(s(s(s(s(s(0(x1)))))))))))) String Reversal Processor: sq(0(x1)) -> p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(x1))))))))))))))))) sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) Matrix Interpretation Processor: dim=1 interpretation: [twice](x0) = x0, [p](x0) = x0, [s](x0) = x0, [sq](x0) = x0 + 5, [0](x0) = x0 + 4 orientation: sq(0(x1)) = x1 + 9 >= x1 + 4 = p(s(p(s(p(p(p(p(s(s(s(s(0(p(s(p(s(x1))))))))))))))))) sq(s(x1)) = x1 + 5 >= x1 + 5 = s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) = x1 + 4 >= x1 + 4 = p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) = x1 >= x1 = p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) = x1 >= x1 = p(x1) p(s(x1)) = x1 >= x1 = x1 p(0(x1)) = x1 + 4 >= x1 + 4 = 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) problem: sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) DP Processor: DPs: sq#(s(x1)) -> p#(s(s(s(s(s(s(x1))))))) sq#(s(x1)) -> p#(p(s(s(s(s(s(s(x1)))))))) sq#(s(x1)) -> p#(p(p(s(s(s(s(s(s(x1))))))))) sq#(s(x1)) -> p#(p(p(p(s(s(s(s(s(s(x1)))))))))) sq#(s(x1)) -> p#(p(p(p(p(s(s(s(s(s(s(x1))))))))))) sq#(s(x1)) -> p#(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) sq#(s(x1)) -> p#(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))) sq#(s(x1)) -> p#(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))) sq#(s(x1)) -> p#(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))) sq#(s(x1)) -> p#(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) sq#(s(x1)) -> p#(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))) sq#(s(x1)) -> p#(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))))) twice#(0(x1)) -> p#(s(x1)) twice#(0(x1)) -> p#(s(p(s(x1)))) twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice#(s(x1)) -> p#(s(x1)) twice#(s(x1)) -> p#(s(p(s(x1)))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p#(p(s(x1))) -> p#(x1) TRS: sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) TDG Processor: DPs: sq#(s(x1)) -> p#(s(s(s(s(s(s(x1))))))) sq#(s(x1)) -> p#(p(s(s(s(s(s(s(x1)))))))) sq#(s(x1)) -> p#(p(p(s(s(s(s(s(s(x1))))))))) sq#(s(x1)) -> p#(p(p(p(s(s(s(s(s(s(x1)))))))))) sq#(s(x1)) -> p#(p(p(p(p(s(s(s(s(s(s(x1))))))))))) sq#(s(x1)) -> p#(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) sq#(s(x1)) -> p#(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))) sq#(s(x1)) -> p#(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))) sq#(s(x1)) -> p#(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))) sq#(s(x1)) -> p#(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) sq#(s(x1)) -> p#(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))) sq#(s(x1)) -> p#(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))))) twice#(0(x1)) -> p#(s(x1)) twice#(0(x1)) -> p#(s(p(s(x1)))) twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice#(s(x1)) -> p#(s(x1)) twice#(s(x1)) -> p#(s(p(s(x1)))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p#(p(s(x1))) -> p#(x1) TRS: sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) graph: twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> twice#(p(s(p(s(x1))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(s(p(s(x1)))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(s(x1)) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(p(s(x1)))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(x1)) twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(s(p(s(x1)))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(s(x1)) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(s(p(s(x1)))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(s(x1)) -> p#(p(s(x1))) -> p#(x1) p#(p(s(x1))) -> p#(x1) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> twice#(p(s(p(s(x1))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(p(s(x1)))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(x1)) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(p(s(x1)))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(x1)) sq#(s(x1)) -> p#(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(p(p(s(s(s(s(s(s(x1))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(p(s(s(s(s(s(s(x1)))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(s(s(s(s(s(s(x1))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(s(s(s(s(s(s(x1)))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(s(s(s(s(s(s(x1))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(p(p(s(s(s(s(s(s(x1))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(p(s(s(s(s(s(s(x1)))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(s(s(s(s(s(s(x1))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(s(s(s(s(s(s(x1)))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(s(s(s(s(s(x1))))))) EDG Processor: DPs: sq#(s(x1)) -> p#(s(s(s(s(s(s(x1))))))) sq#(s(x1)) -> p#(p(s(s(s(s(s(s(x1)))))))) sq#(s(x1)) -> p#(p(p(s(s(s(s(s(s(x1))))))))) sq#(s(x1)) -> p#(p(p(p(s(s(s(s(s(s(x1)))))))))) sq#(s(x1)) -> p#(p(p(p(p(s(s(s(s(s(s(x1))))))))))) sq#(s(x1)) -> p#(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) sq#(s(x1)) -> p#(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))) sq#(s(x1)) -> p#(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))) sq#(s(x1)) -> p#(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))) sq#(s(x1)) -> p#(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) sq#(s(x1)) -> p#(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))) sq#(s(x1)) -> p#(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))) sq#(s(x1)) -> p#(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))))) twice#(0(x1)) -> p#(s(x1)) twice#(0(x1)) -> p#(s(p(s(x1)))) twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice#(s(x1)) -> p#(s(x1)) twice#(s(x1)) -> p#(s(p(s(x1)))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p#(p(s(x1))) -> p#(x1) TRS: sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) graph: twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(x1)) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(p(s(x1)))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) twice#(s(x1)) -> twice#(p(s(p(s(x1))))) -> twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) -> p#(p(s(x1))) -> p#(x1) p#(p(s(x1))) -> p#(x1) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(x1)) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(p(s(x1)))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(p(s(p(s(x1)))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(p(s(p(s(p(s(x1))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(s(s(p(s(p(s(p(s(x1)))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1)))))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(0(x1)) -> p#(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(x1)) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(p(s(x1)))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> twice#(p(s(p(s(x1))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(twice(p(s(p(s(x1))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(twice(p(s(p(s(x1)))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1)))))))))))))) sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) sq#(s(x1)) -> p#(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(p(p(s(s(s(s(s(s(x1))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(p(s(s(s(s(s(s(x1)))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(s(s(s(s(s(s(x1))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(s(s(s(s(s(s(x1)))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> p#(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(s(s(s(s(s(x1))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(s(s(s(s(s(s(x1)))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(s(s(s(s(s(s(x1))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(p(s(s(s(s(s(s(x1)))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(p(p(s(s(s(s(s(s(x1))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))) sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) -> sq#(s(x1)) -> p#(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1)))))))))))))))))))))))))))))))) SCC Processor: #sccs: 2 #rules: 2 #arcs: 69/1444 DPs: sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) TRS: sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) Usable Rule Processor: DPs: sq#(s(x1)) -> sq#(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))) TRS: p(s(x1)) -> x1 p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: f80() -> 2* sq{#,0}(14) -> 1* p0(10) -> 11* p0(12) -> 13* p0(9) -> 10* p0(11) -> 12* p0(13) -> 14* p0(8) -> 9* s0(5) -> 6* s0(7) -> 8* s0(2) -> 3* s0(4) -> 5* s0(6) -> 7* s0(3) -> 4* 2 -> 14* 3 -> 13* 4 -> 12* 5 -> 11* 6 -> 10* 7 -> 9* problem: DPs: TRS: p(s(x1)) -> x1 p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) Qed DPs: p#(p(s(x1))) -> p#(x1) TRS: sq(s(x1)) -> s(p(s(p(s(p(p(s(s(twice(p(s(p(s(p(p(p(s(s(s(sq(p(p(p(p(p(p(s(s(s(s(s(s(x1))))))))))))))))))))))))))))))))) twice(0(x1)) -> p(p(p(p(s(s(p(s(s(s(0(p(p(p(s(s(s(p(p(s(s(p(s(p(s(p(s(x1))))))))))))))))))))))))))) twice(s(x1)) -> p(p(s(s(s(p(p(s(s(s(twice(p(s(p(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(s(s(s(x1)))))))))))) Usable Rule Processor: DPs: p#(p(s(x1))) -> p#(x1) TRS: Arctic Interpretation Processor: dimension: 1 usable rules: interpretation: [p#](x0) = 6x0, [p](x0) = 1x0 + 12, [s](x0) = x0 + 9 orientation: p#(p(s(x1))) = 7x1 + 18 >= 6x1 = p#(x1) problem: DPs: TRS: Qed