Abstract
Termination and innermost termination are shown to be decidable for term rewrite systems whose right-hand side terms are restricted to be shallow (variables occur at depth at most one) and linear. Innermost termination is also shown to be decidable for shallow rewrite systems. In all cases, we show that nontermination implies nontermination starting from flat terms. The proof is completed by using the useful enabling result that, for right shallow rewrite systems, existence of nonterminating derivations starting from a given term is decidable. We also show that termination is undecidable for shallow rewrite systems. For right-shallow systems, general and innermost termination are both undecidable.
The first two authors were supported by Spanish Min. of Educ. and Science by the LogicTools project (TIN2004-03382). The second author was also supported by Spanish Min. of Educ. and Science by the GRAMMARS project (TIN2004-07925-C03-01). The third author was supported in part by the National Science Foundation under grant CCR-0326540.
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Bradley, A.R., Manna, Z., Sipma, H.B.: The polyranking principle. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1349–1361. Springer, Heidelberg (2005)
Cook, B., Podelski, A., Rybalchenko, A.: Termination proofs for systems code. In: Proc. ACM SIGPLAN 2006 Conf. Prog. Lang. Design and Impl. PLDI, pp. 415–426. ACM, New York (2006)
Dershowitz, N.: Termination of linear rewriting systems. In: Even, S., Kariv, O. (eds.) Automata, Languages and Programming. LNCS, vol. 115, pp. 448–458. Springer, Heidelberg (1981)
Godoy, G., Tiwari, A.: Deciding fundamental properties of right-(ground or variable) rewrite systems by rewrite closure. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 91–106. Springer, Heidelberg (2004)
Godoy, G., Tiwari, A.: Termination of rewrite systems with shallow right-linear, collapsing, and right-ground rules. In: Nieuwenhuis, R. (ed.) Automated Deduction – CADE-20. LNCS (LNAI), vol. 3632, pp. 164–176. Springer, Heidelberg (2005)
Hart, S., Sharir, M., Pnueli, A.: Termination of probabilistic concurrent program. ACM Trans. Program. Lang. Syst. 5(3), 356–380 (1983)
Huet, G., Lankford, D.S.: On the uniform halting problem for term rewriting systems. INRIA, Le Chesnay, France, Technical Report 283 (1978)
Mitsuhashi, I., Oyamaguchi, M., Jacquemard, F.: The confluence problem for flat TRSs. In: Calmet, J., Ida, T., Wang, D. (eds.) AISC 2006. LNCS (LNAI), vol. 4120, pp. 68–81. Springer, Heidelberg (2006)
Plaisted, D.A.: Polynomial time termination and constraint satisfaction tests. In: Kirchner, C. (ed.) Rewriting Techniques and Applications. LNCS, vol. 690, pp. 405–420. Springer, Heidelberg (1993)
Takai, T., Kaji, Y., Seki, H.: Right-linear finite path overlapping term rewriting systems effectively preserve recognizability. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 246–260. Springer, Heidelberg (2000)
Tiwari, A.: Termination of linear programs. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 70–82. Springer, Heidelberg (2004)
Toyama, Y.: Counterexamples to termination for the direct sum of term rewriting systems. Information Processing Letters 25, 141–143 (1987)
Wang, Y., Sakai, M.: Decidability of termination for semi-constructor trss, left-linear shallow trss and related systems. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 343–356. Springer, Heidelberg (2006)
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Godoy, G., Huntingford, E., Tiwari, A. (2007). Termination of Rewriting with Right-Flat Rules . In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_16
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DOI: https://doi.org/10.1007/978-3-540-73449-9_16
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