(0) Obligation:

Clauses:

rev(L, R) :- rev(L, [], R).
rev([], Y, Z) :- ','(!, eq(Y, Z)).
rev(L, S, R) :- ','(head(L, X), ','(tail(L, T), rev(T, .(X, S), R))).
head([], X1).
head(.(X, X2), X).
tail([], []).
tail(.(X3, Xs), Xs).
eq(X, X).

Queries:

rev(g,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

(2) Obligation:

Clauses:

rev116([], T138, T139, .(T138, T139)).
rev116(.(T147, T148), T141, T142, T144) :- rev116(T148, T147, .(T141, T142), T144).
rev1([], []).
rev1(.(T18, []), .(T18, [])).
rev1(.(T32, .(T31, [])), .(T31, .(T32, []))).
rev1(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))).
rev1(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))).
rev1(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))).
rev1(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))).
rev1(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)).
rev1(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) :- rev116(T148, T147, .(T141, T142), T144).

Queries:

rev1(g,a).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
rev1_in: (b,f)
rev116_in: (b,f,f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

The argument filtering Pi contains the following mapping:
rev1_in_ga(x1, x2)  =  rev1_in_ga(x1)
[]  =  []
rev1_out_ga(x1, x2)  =  rev1_out_ga
.(x1, x2)  =  .(x2)
U2_ga(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_ga(x11)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

The argument filtering Pi contains the following mapping:
rev1_in_ga(x1, x2)  =  rev1_in_ga(x1)
[]  =  []
rev1_out_ga(x1, x2)  =  rev1_out_ga
.(x1, x2)  =  .(x2)
U2_ga(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_ga(x11)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)

(5) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

REV1_IN_GA(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_GA(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV1_IN_GA(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → U1_GAAA(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

The argument filtering Pi contains the following mapping:
rev1_in_ga(x1, x2)  =  rev1_in_ga(x1)
[]  =  []
rev1_out_ga(x1, x2)  =  rev1_out_ga
.(x1, x2)  =  .(x2)
U2_ga(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_ga(x11)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)
REV1_IN_GA(x1, x2)  =  REV1_IN_GA(x1)
U2_GA(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_GA(x11)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_IN_GAAA(x1)
U1_GAAA(x1, x2, x3, x4, x5, x6)  =  U1_GAAA(x6)

We have to consider all (P,R,Pi)-chains

(6) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

REV1_IN_GA(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_GA(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV1_IN_GA(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → U1_GAAA(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

The argument filtering Pi contains the following mapping:
rev1_in_ga(x1, x2)  =  rev1_in_ga(x1)
[]  =  []
rev1_out_ga(x1, x2)  =  rev1_out_ga
.(x1, x2)  =  .(x2)
U2_ga(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_ga(x11)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)
REV1_IN_GA(x1, x2)  =  REV1_IN_GA(x1)
U2_GA(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_GA(x11)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_IN_GAAA(x1)
U1_GAAA(x1, x2, x3, x4, x5, x6)  =  U1_GAAA(x6)

We have to consider all (P,R,Pi)-chains

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 3 less nodes.

(8) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

The TRS R consists of the following rules:

rev1_in_ga([], []) → rev1_out_ga([], [])
rev1_in_ga(.(T18, []), .(T18, [])) → rev1_out_ga(.(T18, []), .(T18, []))
rev1_in_ga(.(T32, .(T31, [])), .(T31, .(T32, []))) → rev1_out_ga(.(T32, .(T31, [])), .(T31, .(T32, [])))
rev1_in_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, [])))) → rev1_out_ga(.(T49, .(T48, .(T47, []))), .(T47, .(T48, .(T49, []))))
rev1_in_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, []))))) → rev1_out_ga(.(T69, .(T68, .(T67, .(T66, [])))), .(T66, .(T67, .(T68, .(T69, [])))))
rev1_in_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, [])))))) → rev1_out_ga(.(T92, .(T91, .(T90, .(T89, .(T88, []))))), .(T88, .(T89, .(T90, .(T91, .(T92, []))))))
rev1_in_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, []))))))) → rev1_out_ga(.(T118, .(T117, .(T116, .(T115, .(T114, .(T113, [])))))), .(T113, .(T114, .(T115, .(T116, .(T117, .(T118, [])))))))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, []))))))), .(T138, T139))
rev1_in_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144) → U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
rev116_in_gaaa([], T138, T139, .(T138, T139)) → rev116_out_gaaa([], T138, T139, .(T138, T139))
rev116_in_gaaa(.(T147, T148), T141, T142, T144) → U1_gaaa(T147, T148, T141, T142, T144, rev116_in_gaaa(T148, T147, .(T141, T142), T144))
U1_gaaa(T147, T148, T141, T142, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev116_out_gaaa(.(T147, T148), T141, T142, T144)
U2_ga(T125, T124, T123, T122, T121, T120, T130, T147, T148, T144, rev116_out_gaaa(T148, T147, .(T141, T142), T144)) → rev1_out_ga(.(T125, .(T124, .(T123, .(T122, .(T121, .(T120, .(T130, .(T147, T148)))))))), T144)

The argument filtering Pi contains the following mapping:
rev1_in_ga(x1, x2)  =  rev1_in_ga(x1)
[]  =  []
rev1_out_ga(x1, x2)  =  rev1_out_ga
.(x1, x2)  =  .(x2)
U2_ga(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)  =  U2_ga(x11)
rev116_in_gaaa(x1, x2, x3, x4)  =  rev116_in_gaaa(x1)
rev116_out_gaaa(x1, x2, x3, x4)  =  rev116_out_gaaa
U1_gaaa(x1, x2, x3, x4, x5, x6)  =  U1_gaaa(x6)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_IN_GAAA(x1)

We have to consider all (P,R,Pi)-chains

(9) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(10) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

REV116_IN_GAAA(.(T147, T148), T141, T142, T144) → REV116_IN_GAAA(T148, T147, .(T141, T142), T144)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x2)
REV116_IN_GAAA(x1, x2, x3, x4)  =  REV116_IN_GAAA(x1)

We have to consider all (P,R,Pi)-chains

(11) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(12) Obligation:

Q DP problem:
The TRS P consists of the following rules:

REV116_IN_GAAA(.(T148)) → REV116_IN_GAAA(T148)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(13) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

  • REV116_IN_GAAA(.(T148)) → REV116_IN_GAAA(T148)
    The graph contains the following edges 1 > 1

(14) TRUE