The rewrite relation of the following TRS is considered.
a__f(0) | → | cons(0,f(s(0))) | (1) |
a__f(s(0)) | → | a__f(a__p(s(0))) | (2) |
a__p(s(0)) | → | 0 | (3) |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(p(X)) | → | a__p(mark(X)) | (5) |
mark(0) | → | 0 | (6) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (7) |
mark(s(X)) | → | s(mark(X)) | (8) |
a__f(X) | → | f(X) | (9) |
a__p(X) | → | p(X) | (10) |
final states:
{0, 1, 2, 3}
transitions:
00 | → | 0 |
cons0(0,0) | → | 0 |
f0(0) | → | 0 |
s0(0) | → | 0 |
p0(0) | → | 0 |
a__f0(0) | → | 1 |
a__p0(0) | → | 2 |
mark0(0) | → | 3 |
01 | → | 4 |
01 | → | 7 |
s1(7) | → | 6 |
f1(6) | → | 5 |
cons1(4,5) | → | 1 |
s1(7) | → | 9 |
a__p1(9) | → | 8 |
a__f1(8) | → | 1 |
01 | → | 2 |
mark1(0) | → | 10 |
a__f1(10) | → | 3 |
mark1(0) | → | 11 |
a__p1(11) | → | 3 |
01 | → | 3 |
mark1(0) | → | 12 |
cons1(12,0) | → | 3 |
mark1(0) | → | 13 |
s1(13) | → | 3 |
f1(0) | → | 1 |
p1(0) | → | 2 |
02 | → | 8 |
a__f1(10) | → | 10 |
a__f1(10) | → | 11 |
a__f1(10) | → | 12 |
a__f1(10) | → | 13 |
a__p1(11) | → | 10 |
a__p1(11) | → | 11 |
a__p1(11) | → | 12 |
a__p1(11) | → | 13 |
01 | → | 10 |
01 | → | 11 |
01 | → | 12 |
01 | → | 13 |
cons1(12,0) | → | 10 |
cons1(12,0) | → | 11 |
cons1(12,0) | → | 12 |
cons1(12,0) | → | 13 |
s1(13) | → | 10 |
s1(13) | → | 11 |
s1(13) | → | 12 |
s1(13) | → | 13 |
f2(8) | → | 1 |
f2(10) | → | 3 |
p2(11) | → | 3 |
p2(9) | → | 8 |
02 | → | 14 |
02 | → | 17 |
s2(17) | → | 16 |
f2(16) | → | 15 |
cons2(14,15) | → | 3 |
cons2(14,15) | → | 10 |
cons2(14,15) | → | 11 |
cons2(14,15) | → | 12 |
cons2(14,15) | → | 13 |
s2(17) | → | 19 |
a__p2(19) | → | 18 |
a__f2(18) | → | 3 |
a__f2(18) | → | 10 |
a__f2(18) | → | 11 |
a__f2(18) | → | 12 |
a__f2(18) | → | 13 |
02 | → | 3 |
02 | → | 10 |
02 | → | 11 |
02 | → | 12 |
02 | → | 13 |
f2(10) | → | 10 |
f2(10) | → | 11 |
f2(10) | → | 12 |
f2(10) | → | 13 |
p2(11) | → | 10 |
p2(11) | → | 11 |
p2(11) | → | 12 |
p2(11) | → | 13 |
cons2(14,15) | → | 1 |
03 | → | 18 |
f3(18) | → | 3 |
f3(18) | → | 10 |
f3(18) | → | 11 |
f3(18) | → | 12 |
f3(18) | → | 13 |
p3(19) | → | 18 |
03 | → | 20 |
03 | → | 23 |
s3(23) | → | 22 |
f3(22) | → | 21 |
cons3(20,21) | → | 3 |
cons3(20,21) | → | 10 |
cons3(20,21) | → | 11 |
cons3(20,21) | → | 12 |
cons3(20,21) | → | 13 |