Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex1_GL02a_GM)
The rewrite relation of the following TRS is considered.
a__eq(0,0) |
→ |
true |
(1) |
a__eq(s(X),s(Y)) |
→ |
a__eq(X,Y) |
(2) |
a__eq(X,Y) |
→ |
false |
(3) |
a__inf(X) |
→ |
cons(X,inf(s(X))) |
(4) |
a__take(0,X) |
→ |
nil |
(5) |
a__take(s(X),cons(Y,L)) |
→ |
cons(Y,take(X,L)) |
(6) |
a__length(nil) |
→ |
0 |
(7) |
a__length(cons(X,L)) |
→ |
s(length(L)) |
(8) |
mark(eq(X1,X2)) |
→ |
a__eq(X1,X2) |
(9) |
mark(inf(X)) |
→ |
a__inf(mark(X)) |
(10) |
mark(take(X1,X2)) |
→ |
a__take(mark(X1),mark(X2)) |
(11) |
mark(length(X)) |
→ |
a__length(mark(X)) |
(12) |
mark(0) |
→ |
0 |
(13) |
mark(true) |
→ |
true |
(14) |
mark(s(X)) |
→ |
s(X) |
(15) |
mark(false) |
→ |
false |
(16) |
mark(cons(X1,X2)) |
→ |
cons(X1,X2) |
(17) |
mark(nil) |
→ |
nil |
(18) |
a__eq(X1,X2) |
→ |
eq(X1,X2) |
(19) |
a__inf(X) |
→ |
inf(X) |
(20) |
a__take(X1,X2) |
→ |
take(X1,X2) |
(21) |
a__length(X) |
→ |
length(X) |
(22) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by NaTT @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
mark#(eq(X1,X2)) |
→ |
a__eq#(X1,X2) |
(23) |
mark#(length(X)) |
→ |
a__length#(mark(X)) |
(24) |
mark#(inf(X)) |
→ |
mark#(X) |
(25) |
mark#(length(X)) |
→ |
mark#(X) |
(26) |
mark#(take(X1,X2)) |
→ |
mark#(X2) |
(27) |
mark#(take(X1,X2)) |
→ |
a__take#(mark(X1),mark(X2)) |
(28) |
a__eq#(s(X),s(Y)) |
→ |
a__eq#(X,Y) |
(29) |
mark#(inf(X)) |
→ |
a__inf#(mark(X)) |
(30) |
mark#(take(X1,X2)) |
→ |
mark#(X1) |
(31) |
1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.