/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: tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) Proof: String Reversal Processor: 0(tower(x1)) -> s(p(s(p(0(s(x1)))))) s(tower(x1)) -> s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 0(twoto(x1)) -> 0(s(x1)) s(twoto(x1)) -> s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 0(twice(x1)) -> 0(x1) s(twice(x1)) -> s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) s(p(p(x1))) -> p(x1) s(p(x1)) -> x1 0(p(x1)) -> s(s(s(s(s(s(s(s(0(x1))))))))) Matrix Interpretation Processor: dim=1 interpretation: [twice](x0) = x0, [twoto](x0) = x0, [p](x0) = x0, [s](x0) = x0, [tower](x0) = 2x0 + 2, [0](x0) = 8x0 + 4 orientation: 0(tower(x1)) = 16x1 + 20 >= 8x1 + 4 = s(p(s(p(0(s(x1)))))) s(tower(x1)) = 2x1 + 2 >= 2x1 + 2 = s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 0(twoto(x1)) = 8x1 + 4 >= 8x1 + 4 = 0(s(x1)) s(twoto(x1)) = x1 >= x1 = s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 0(twice(x1)) = 8x1 + 4 >= 8x1 + 4 = 0(x1) s(twice(x1)) = x1 >= x1 = s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) s(p(p(x1))) = x1 >= x1 = p(x1) s(p(x1)) = x1 >= x1 = x1 0(p(x1)) = 8x1 + 4 >= 8x1 + 4 = s(s(s(s(s(s(s(s(0(x1))))))))) problem: s(tower(x1)) -> s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 0(twoto(x1)) -> 0(s(x1)) s(twoto(x1)) -> s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 0(twice(x1)) -> 0(x1) s(twice(x1)) -> s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) s(p(p(x1))) -> p(x1) s(p(x1)) -> x1 0(p(x1)) -> s(s(s(s(s(s(s(s(0(x1))))))))) String Reversal Processor: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) DP Processor: DPs: tower#(s(x1)) -> p#(s(x1)) tower#(s(x1)) -> p#(s(p(s(x1)))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) tower#(s(x1)) -> p#(s(tower(p(s(p(s(x1))))))) tower#(s(x1)) -> p#(s(p(s(tower(p(s(p(s(x1))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) tower#(s(x1)) -> p#(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) tower#(s(x1)) -> p#(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto#(s(x1)) -> p#(s(x1)) twoto#(s(x1)) -> p#(s(p(s(x1)))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice#(s(x1)) -> p#(s(s(s(x1)))) twice#(s(x1)) -> p#(p(s(s(s(x1))))) twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p#(p(s(x1))) -> p#(x1) TRS: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) TDG Processor: DPs: tower#(s(x1)) -> p#(s(x1)) tower#(s(x1)) -> p#(s(p(s(x1)))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) tower#(s(x1)) -> p#(s(tower(p(s(p(s(x1))))))) tower#(s(x1)) -> p#(s(p(s(tower(p(s(p(s(x1))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) tower#(s(x1)) -> p#(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) tower#(s(x1)) -> p#(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto#(s(x1)) -> p#(s(x1)) twoto#(s(x1)) -> p#(s(p(s(x1)))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice#(s(x1)) -> p#(s(s(s(x1)))) twice#(s(x1)) -> p#(p(s(s(s(x1))))) twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p#(p(s(x1))) -> p#(x1) TRS: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) graph: twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(s(s(s(x1))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(s(s(s(x1)))) twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(s(s(s(x1))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(s(s(s(x1)))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(x1))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(x1)))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(s(x1)))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(x1)) twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(p(s(x1)))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(s(x1)) -> p#(p(s(x1))) -> p#(x1) p#(p(s(x1))) -> p#(x1) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(s(x1)))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(x1)) tower#(s(x1)) -> p#(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> p#(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> p#(s(p(s(tower(p(s(p(s(x1))))))))) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> p#(s(p(s(x1)))) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> p#(s(tower(p(s(p(s(x1))))))) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> p#(s(x1)) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(p(s(tower(p(s(p(s(x1))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(tower(p(s(p(s(x1))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> tower#(p(s(p(s(x1))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(p(s(x1)))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(x1)) EDG Processor: DPs: tower#(s(x1)) -> p#(s(x1)) tower#(s(x1)) -> p#(s(p(s(x1)))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) tower#(s(x1)) -> p#(s(tower(p(s(p(s(x1))))))) tower#(s(x1)) -> p#(s(p(s(tower(p(s(p(s(x1))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) tower#(s(x1)) -> p#(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) tower#(s(x1)) -> p#(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto#(s(x1)) -> p#(s(x1)) twoto#(s(x1)) -> p#(s(p(s(x1)))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice#(s(x1)) -> p#(s(s(s(x1)))) twice#(s(x1)) -> p#(p(s(s(s(x1))))) twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p#(p(s(x1))) -> p#(x1) TRS: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) graph: twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(s(s(s(x1)))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(s(s(s(x1))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) -> p#(p(s(x1))) -> p#(x1) twice#(s(x1)) -> p#(p(s(s(s(x1))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(x1)))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(x1))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(x1)))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) -> twice#(s(x1)) -> p#(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(x1)) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(s(x1)))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) -> twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) -> p#(p(s(x1))) -> p#(x1) p#(p(s(x1))) -> p#(x1) -> p#(p(s(x1))) -> p#(x1) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(x1)) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(s(x1)))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(s(twoto(p(s(p(s(x1))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(s(s(s(twoto(p(s(p(s(x1)))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> twice#(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) -> twoto#(s(x1)) -> p#(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(x1)) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(p(s(x1)))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> tower#(p(s(p(s(x1))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(tower(p(s(p(s(x1))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(p(s(tower(p(s(p(s(x1))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> twoto#(p(s(p(s(tower(p(s(p(s(x1)))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) tower#(s(x1)) -> tower#(p(s(p(s(x1))))) -> tower#(s(x1)) -> p#(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) SCC Processor: #sccs: 4 #rules: 4 #arcs: 65/1089 DPs: tower#(s(x1)) -> tower#(p(s(p(s(x1))))) TRS: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) Usable Rule Processor: DPs: tower#(s(x1)) -> tower#(p(s(p(s(x1))))) TRS: p(s(x1)) -> x1 Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: f100() -> 2* tower{#,0}(6) -> 1* p0(5) -> 6* p0(3) -> 4* s0(2) -> 3* s0(4) -> 5* 2 -> 4* 4 -> 6* problem: DPs: TRS: p(s(x1)) -> x1 Qed DPs: twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) TRS: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) Usable Rule Processor: DPs: twoto#(s(x1)) -> twoto#(p(s(p(s(x1))))) TRS: p(s(x1)) -> x1 Arctic Interpretation Processor: dimension: 1 usable rules: p(s(x1)) -> x1 interpretation: [twoto#](x0) = x0 + 4, [p](x0) = -14x0 + 1, [s](x0) = 15x0 + 6 orientation: twoto#(s(x1)) = 15x1 + 6 >= 2x1 + 4 = twoto#(p(s(p(s(x1))))) p(s(x1)) = 1x1 + 1 >= x1 = x1 problem: DPs: TRS: p(s(x1)) -> x1 Qed DPs: twice#(s(x1)) -> twice#(p(p(p(s(s(s(x1))))))) TRS: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) Usable Rule Processor: DPs: twice#(s(x1)) -> twice#(p(p(p(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(x1))))))))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: f150() -> 2* twice{#,0}(8) -> 1* p0(5) -> 6* p0(7) -> 8* p0(6) -> 7* s0(2) -> 3* s0(4) -> 5* s0(3) -> 4* 2 -> 8* 3 -> 7* 4 -> 6* 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(x1))))))))) Qed DPs: p#(p(s(x1))) -> p#(x1) TRS: tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 p(0(x1)) -> 0(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