Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex15_Luc98_GM)
The rewrite relation of the following TRS is considered.
a__and(true,X) |
→ |
mark(X) |
(1) |
a__and(false,Y) |
→ |
false |
(2) |
a__if(true,X,Y) |
→ |
mark(X) |
(3) |
a__if(false,X,Y) |
→ |
mark(Y) |
(4) |
a__add(0,X) |
→ |
mark(X) |
(5) |
a__add(s(X),Y) |
→ |
s(add(X,Y)) |
(6) |
a__first(0,X) |
→ |
nil |
(7) |
a__first(s(X),cons(Y,Z)) |
→ |
cons(Y,first(X,Z)) |
(8) |
a__from(X) |
→ |
cons(X,from(s(X))) |
(9) |
mark(and(X1,X2)) |
→ |
a__and(mark(X1),X2) |
(10) |
mark(if(X1,X2,X3)) |
→ |
a__if(mark(X1),X2,X3) |
(11) |
mark(add(X1,X2)) |
→ |
a__add(mark(X1),X2) |
(12) |
mark(first(X1,X2)) |
→ |
a__first(mark(X1),mark(X2)) |
(13) |
mark(from(X)) |
→ |
a__from(X) |
(14) |
mark(true) |
→ |
true |
(15) |
mark(false) |
→ |
false |
(16) |
mark(0) |
→ |
0 |
(17) |
mark(s(X)) |
→ |
s(X) |
(18) |
mark(nil) |
→ |
nil |
(19) |
mark(cons(X1,X2)) |
→ |
cons(X1,X2) |
(20) |
a__and(X1,X2) |
→ |
and(X1,X2) |
(21) |
a__if(X1,X2,X3) |
→ |
if(X1,X2,X3) |
(22) |
a__add(X1,X2) |
→ |
add(X1,X2) |
(23) |
a__first(X1,X2) |
→ |
first(X1,X2) |
(24) |
a__from(X) |
→ |
from(X) |
(25) |
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#(first(X1,X2)) |
→ |
mark#(X1) |
(26) |
mark#(add(X1,X2)) |
→ |
a__add#(mark(X1),X2) |
(27) |
a__and#(true,X) |
→ |
mark#(X) |
(28) |
mark#(and(X1,X2)) |
→ |
a__and#(mark(X1),X2) |
(29) |
a__add#(0,X) |
→ |
mark#(X) |
(30) |
a__if#(true,X,Y) |
→ |
mark#(X) |
(31) |
a__if#(false,X,Y) |
→ |
mark#(Y) |
(32) |
mark#(add(X1,X2)) |
→ |
mark#(X1) |
(33) |
mark#(and(X1,X2)) |
→ |
mark#(X1) |
(34) |
mark#(if(X1,X2,X3)) |
→ |
mark#(X1) |
(35) |
mark#(first(X1,X2)) |
→ |
mark#(X2) |
(36) |
mark#(first(X1,X2)) |
→ |
a__first#(mark(X1),mark(X2)) |
(37) |
mark#(from(X)) |
→ |
a__from#(X) |
(38) |
mark#(if(X1,X2,X3)) |
→ |
a__if#(mark(X1),X2,X3) |
(39) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.