The rewrite relation of the following TRS is considered.
a(x1) | → | x1 | (1) |
a(b(x1)) | → | x1 | (2) |
a(c(c(x1))) | → | c(b(c(a(c(a(x1)))))) | (3) |
{c(☐), b(☐), a(☐)}
We obtain the transformed TRSc(a(x1)) | → | c(x1) | (4) |
c(a(b(x1))) | → | c(x1) | (5) |
c(a(c(c(x1)))) | → | c(c(b(c(a(c(a(x1))))))) | (6) |
b(a(x1)) | → | b(x1) | (7) |
b(a(b(x1))) | → | b(x1) | (8) |
b(a(c(c(x1)))) | → | b(c(b(c(a(c(a(x1))))))) | (9) |
a(a(x1)) | → | a(x1) | (10) |
a(a(b(x1))) | → | a(x1) | (11) |
a(a(c(c(x1)))) | → | a(c(b(c(a(c(a(x1))))))) | (12) |
As carrier we take the set {0,1,2}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 3):
[c(x1)] | = | 3x1 + 0 |
[b(x1)] | = | 3x1 + 1 |
[a(x1)] | = | 3x1 + 2 |
a2(a2(x1)) | → | a2(x1) | (13) |
a2(a1(x1)) | → | a1(x1) | (14) |
a2(a0(x1)) | → | a0(x1) | (15) |
b2(a2(x1)) | → | b2(x1) | (16) |
b2(a1(x1)) | → | b1(x1) | (17) |
b2(a0(x1)) | → | b0(x1) | (18) |
c2(a2(x1)) | → | c2(x1) | (19) |
c2(a1(x1)) | → | c1(x1) | (20) |
c2(a0(x1)) | → | c0(x1) | (21) |
a2(a1(b2(x1))) | → | a2(x1) | (22) |
a2(a1(b1(x1))) | → | a1(x1) | (23) |
a2(a1(b0(x1))) | → | a0(x1) | (24) |
b2(a1(b2(x1))) | → | b2(x1) | (25) |
b2(a1(b1(x1))) | → | b1(x1) | (26) |
b2(a1(b0(x1))) | → | b0(x1) | (27) |
c2(a1(b2(x1))) | → | c2(x1) | (28) |
c2(a1(b1(x1))) | → | c1(x1) | (29) |
c2(a1(b0(x1))) | → | c0(x1) | (30) |
a2(a0(c0(c2(x1)))) | → | a0(c1(b0(c2(a0(c2(a2(x1))))))) | (31) |
a2(a0(c0(c1(x1)))) | → | a0(c1(b0(c2(a0(c2(a1(x1))))))) | (32) |
a2(a0(c0(c0(x1)))) | → | a0(c1(b0(c2(a0(c2(a0(x1))))))) | (33) |
b2(a0(c0(c2(x1)))) | → | b0(c1(b0(c2(a0(c2(a2(x1))))))) | (34) |
b2(a0(c0(c1(x1)))) | → | b0(c1(b0(c2(a0(c2(a1(x1))))))) | (35) |
b2(a0(c0(c0(x1)))) | → | b0(c1(b0(c2(a0(c2(a0(x1))))))) | (36) |
c2(a0(c0(c2(x1)))) | → | c0(c1(b0(c2(a0(c2(a2(x1))))))) | (37) |
c2(a0(c0(c1(x1)))) | → | c0(c1(b0(c2(a0(c2(a1(x1))))))) | (38) |
c2(a0(c0(c0(x1)))) | → | c0(c1(b0(c2(a0(c2(a0(x1))))))) | (39) |
[c0(x1)] | = |
x1 +
|
||||
[c1(x1)] | = |
x1 +
|
||||
[c2(x1)] | = |
x1 +
|
||||
[b0(x1)] | = |
x1 +
|
||||
[b1(x1)] | = |
x1 +
|
||||
[b2(x1)] | = |
x1 +
|
||||
[a0(x1)] | = |
x1 +
|
||||
[a1(x1)] | = |
x1 +
|
||||
[a2(x1)] | = |
x1 +
|
b2(a1(x1)) | → | b1(x1) | (17) |
b2(a0(x1)) | → | b0(x1) | (18) |
a2(a1(b2(x1))) | → | a2(x1) | (22) |
a2(a1(b1(x1))) | → | a1(x1) | (23) |
b2(a1(b2(x1))) | → | b2(x1) | (25) |
b2(a1(b1(x1))) | → | b1(x1) | (26) |
b2(a1(b0(x1))) | → | b0(x1) | (27) |
c2(a1(b2(x1))) | → | c2(x1) | (28) |
c2(a1(b1(x1))) | → | c1(x1) | (29) |
b2(a0(c0(c2(x1)))) | → | b0(c1(b0(c2(a0(c2(a2(x1))))))) | (34) |
b2(a0(c0(c1(x1)))) | → | b0(c1(b0(c2(a0(c2(a1(x1))))))) | (35) |
b2(a0(c0(c0(x1)))) | → | b0(c1(b0(c2(a0(c2(a0(x1))))))) | (36) |
a2(a2(x1)) | → | a2(x1) | (13) |
a1(a2(x1)) | → | a1(x1) | (40) |
a0(a2(x1)) | → | a0(x1) | (41) |
a2(b2(x1)) | → | b2(x1) | (42) |
a2(c2(x1)) | → | c2(x1) | (43) |
a1(c2(x1)) | → | c1(x1) | (44) |
a0(c2(x1)) | → | c0(x1) | (45) |
b0(a1(a2(x1))) | → | a0(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(c0(a0(a2(x1)))) | → | a2(c2(a0(c2(b0(c1(a0(x1))))))) | (48) |
c1(c0(a0(a2(x1)))) | → | a1(c2(a0(c2(b0(c1(a0(x1))))))) | (49) |
c0(c0(a0(a2(x1)))) | → | a0(c2(a0(c2(b0(c1(a0(x1))))))) | (50) |
c2(c0(a0(c2(x1)))) | → | a2(c2(a0(c2(b0(c1(c0(x1))))))) | (51) |
c1(c0(a0(c2(x1)))) | → | a1(c2(a0(c2(b0(c1(c0(x1))))))) | (52) |
c0(c0(a0(c2(x1)))) | → | a0(c2(a0(c2(b0(c1(c0(x1))))))) | (53) |
c0#(c0(a0(c2(x1)))) | → | c0#(x1) | (54) |
c0#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (55) |
c0#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (56) |
c0#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (57) |
c0#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (58) |
c0#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (59) |
c0#(c0(a0(c2(x1)))) | → | a0#(c2(a0(c2(b0(c1(c0(x1))))))) | (60) |
c0#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (61) |
c0#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (62) |
c0#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (63) |
c0#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (64) |
c0#(c0(a0(a2(x1)))) | → | a0#(x1) | (65) |
c0#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (66) |
c0#(c0(a0(a2(x1)))) | → | a0#(c2(a0(c2(b0(c1(a0(x1))))))) | (67) |
c1#(c0(a0(c2(x1)))) | → | c0#(x1) | (68) |
c1#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (69) |
c1#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (70) |
c1#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (71) |
c1#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (72) |
c1#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (73) |
c1#(c0(a0(c2(x1)))) | → | a1#(c2(a0(c2(b0(c1(c0(x1))))))) | (74) |
c1#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (75) |
c1#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (76) |
c1#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (77) |
c1#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (78) |
c1#(c0(a0(a2(x1)))) | → | a0#(x1) | (79) |
c1#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (80) |
c1#(c0(a0(a2(x1)))) | → | a1#(c2(a0(c2(b0(c1(a0(x1))))))) | (81) |
c2#(c0(a0(c2(x1)))) | → | c0#(x1) | (82) |
c2#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (83) |
c2#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (84) |
c2#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (85) |
c2#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (86) |
c2#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (87) |
c2#(c0(a0(c2(x1)))) | → | a2#(c2(a0(c2(b0(c1(c0(x1))))))) | (88) |
c2#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (89) |
c2#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (90) |
c2#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (91) |
c2#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (92) |
c2#(c0(a0(a2(x1)))) | → | a0#(x1) | (93) |
c2#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (94) |
c2#(c0(a0(a2(x1)))) | → | a2#(c2(a0(c2(b0(c1(a0(x1))))))) | (95) |
b0#(a1(c2(x1))) | → | c0#(x1) | (96) |
b0#(a1(a2(x1))) | → | a0#(x1) | (97) |
a0#(c2(x1)) | → | c0#(x1) | (98) |
a0#(a2(x1)) | → | a0#(x1) | (99) |
a1#(c2(x1)) | → | c1#(x1) | (100) |
a1#(a2(x1)) | → | a1#(x1) | (101) |
[c0(x1)] | = |
x1 +
|
||||
[c1(x1)] | = |
x1 +
|
||||
[c2(x1)] | = |
x1 +
|
||||
[b0(x1)] | = |
x1 +
|
||||
[b2(x1)] | = |
x1 +
|
||||
[a0(x1)] | = |
x1 +
|
||||
[a1(x1)] | = |
x1 +
|
||||
[a2(x1)] | = |
x1 +
|
||||
[c0#(x1)] | = |
x1 +
|
||||
[c1#(x1)] | = |
x1 +
|
||||
[c2#(x1)] | = |
x1 +
|
||||
[b0#(x1)] | = |
x1 +
|
||||
[a0#(x1)] | = |
x1 +
|
||||
[a1#(x1)] | = |
x1 +
|
||||
[a2#(x1)] | = |
x1 +
|
a2(a2(x1)) | → | a2(x1) | (13) |
a1(a2(x1)) | → | a1(x1) | (40) |
a0(a2(x1)) | → | a0(x1) | (41) |
a2(b2(x1)) | → | b2(x1) | (42) |
a2(c2(x1)) | → | c2(x1) | (43) |
a1(c2(x1)) | → | c1(x1) | (44) |
a0(c2(x1)) | → | c0(x1) | (45) |
b0(a1(a2(x1))) | → | a0(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(c0(a0(a2(x1)))) | → | a2(c2(a0(c2(b0(c1(a0(x1))))))) | (48) |
c1(c0(a0(a2(x1)))) | → | a1(c2(a0(c2(b0(c1(a0(x1))))))) | (49) |
c0(c0(a0(a2(x1)))) | → | a0(c2(a0(c2(b0(c1(a0(x1))))))) | (50) |
c2(c0(a0(c2(x1)))) | → | a2(c2(a0(c2(b0(c1(c0(x1))))))) | (51) |
c1(c0(a0(c2(x1)))) | → | a1(c2(a0(c2(b0(c1(c0(x1))))))) | (52) |
c0(c0(a0(c2(x1)))) | → | a0(c2(a0(c2(b0(c1(c0(x1))))))) | (53) |
c2#(c0(a0(c2(x1)))) | → | a2#(c2(a0(c2(b0(c1(c0(x1))))))) | (88) |
c2#(c0(a0(a2(x1)))) | → | a2#(c2(a0(c2(b0(c1(a0(x1))))))) | (95) |
The dependency pairs are split into 1 component.
c0#(c0(a0(c2(x1)))) | → | c0#(x1) | (54) |
c0#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (55) |
c1#(c0(a0(c2(x1)))) | → | c0#(x1) | (68) |
c0#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (56) |
c2#(c0(a0(c2(x1)))) | → | c0#(x1) | (82) |
c0#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (57) |
c2#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (83) |
c1#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (69) |
c1#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (70) |
c2#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (84) |
c2#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (85) |
c2#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (86) |
b0#(a1(c2(x1))) | → | c0#(x1) | (96) |
c0#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (58) |
b0#(a1(a2(x1))) | → | a0#(x1) | (97) |
a0#(c2(x1)) | → | c0#(x1) | (98) |
c0#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (59) |
a0#(a2(x1)) | → | a0#(x1) | (99) |
c0#(c0(a0(c2(x1)))) | → | a0#(c2(a0(c2(b0(c1(c0(x1))))))) | (60) |
c0#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (61) |
c1#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (71) |
c2#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (87) |
c2#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (89) |
c1#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (72) |
c1#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (73) |
c1#(c0(a0(c2(x1)))) | → | a1#(c2(a0(c2(b0(c1(c0(x1))))))) | (74) |
a1#(c2(x1)) | → | c1#(x1) | (100) |
c1#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (75) |
c1#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (76) |
c2#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (90) |
c2#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (91) |
c2#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (92) |
c2#(c0(a0(a2(x1)))) | → | a0#(x1) | (93) |
c2#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (94) |
c1#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (77) |
c1#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (78) |
c1#(c0(a0(a2(x1)))) | → | a0#(x1) | (79) |
c1#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (80) |
c1#(c0(a0(a2(x1)))) | → | a1#(c2(a0(c2(b0(c1(a0(x1))))))) | (81) |
a1#(a2(x1)) | → | a1#(x1) | (101) |
c0#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (62) |
c0#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (63) |
c0#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (64) |
c0#(c0(a0(a2(x1)))) | → | a0#(x1) | (65) |
c0#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (66) |
c0#(c0(a0(a2(x1)))) | → | a0#(c2(a0(c2(b0(c1(a0(x1))))))) | (67) |
[c0(x1)] | = |
|
||||||||||||
[c1(x1)] | = |
|
||||||||||||
[c2(x1)] | = |
|
||||||||||||
[b0(x1)] | = |
|
||||||||||||
[b2(x1)] | = |
|
||||||||||||
[a0(x1)] | = |
|
||||||||||||
[a1(x1)] | = |
|
||||||||||||
[a2(x1)] | = |
|
||||||||||||
[c0#(x1)] | = |
|
||||||||||||
[c1#(x1)] | = |
|
||||||||||||
[c2#(x1)] | = |
|
||||||||||||
[b0#(x1)] | = |
|
||||||||||||
[a0#(x1)] | = |
|
||||||||||||
[a1#(x1)] | = |
|
a2(a2(x1)) | → | a2(x1) | (13) |
a1(a2(x1)) | → | a1(x1) | (40) |
a0(a2(x1)) | → | a0(x1) | (41) |
a2(b2(x1)) | → | b2(x1) | (42) |
a2(c2(x1)) | → | c2(x1) | (43) |
a1(c2(x1)) | → | c1(x1) | (44) |
a0(c2(x1)) | → | c0(x1) | (45) |
b0(a1(a2(x1))) | → | a0(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(c0(a0(a2(x1)))) | → | a2(c2(a0(c2(b0(c1(a0(x1))))))) | (48) |
c1(c0(a0(a2(x1)))) | → | a1(c2(a0(c2(b0(c1(a0(x1))))))) | (49) |
c0(c0(a0(a2(x1)))) | → | a0(c2(a0(c2(b0(c1(a0(x1))))))) | (50) |
c2(c0(a0(c2(x1)))) | → | a2(c2(a0(c2(b0(c1(c0(x1))))))) | (51) |
c1(c0(a0(c2(x1)))) | → | a1(c2(a0(c2(b0(c1(c0(x1))))))) | (52) |
c0(c0(a0(c2(x1)))) | → | a0(c2(a0(c2(b0(c1(c0(x1))))))) | (53) |
c0#(c0(a0(c2(x1)))) | → | c0#(x1) | (54) |
c0#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (55) |
c1#(c0(a0(c2(x1)))) | → | c0#(x1) | (68) |
c0#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (56) |
c2#(c0(a0(c2(x1)))) | → | c0#(x1) | (82) |
c0#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (57) |
c2#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (83) |
c1#(c0(a0(c2(x1)))) | → | c1#(c0(x1)) | (69) |
c1#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (70) |
c2#(c0(a0(c2(x1)))) | → | c2#(b0(c1(c0(x1)))) | (84) |
c2#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (85) |
c2#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (86) |
b0#(a1(c2(x1))) | → | c0#(x1) | (96) |
c0#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (58) |
b0#(a1(a2(x1))) | → | a0#(x1) | (97) |
c0#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (59) |
c0#(c0(a0(c2(x1)))) | → | a0#(c2(a0(c2(b0(c1(c0(x1))))))) | (60) |
c0#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (61) |
c1#(c0(a0(c2(x1)))) | → | c2#(a0(c2(b0(c1(c0(x1)))))) | (71) |
c2#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (87) |
c2#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (89) |
c1#(c0(a0(c2(x1)))) | → | b0#(c1(c0(x1))) | (72) |
c1#(c0(a0(c2(x1)))) | → | a0#(c2(b0(c1(c0(x1))))) | (73) |
c1#(c0(a0(a2(x1)))) | → | c1#(a0(x1)) | (75) |
c1#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (76) |
c2#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (90) |
c2#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (91) |
c2#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (92) |
c2#(c0(a0(a2(x1)))) | → | a0#(x1) | (93) |
c2#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (94) |
c1#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (77) |
c1#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (78) |
c1#(c0(a0(a2(x1)))) | → | a0#(x1) | (79) |
c1#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (80) |
c0#(c0(a0(a2(x1)))) | → | c2#(b0(c1(a0(x1)))) | (62) |
c0#(c0(a0(a2(x1)))) | → | c2#(a0(c2(b0(c1(a0(x1)))))) | (63) |
c0#(c0(a0(a2(x1)))) | → | b0#(c1(a0(x1))) | (64) |
c0#(c0(a0(a2(x1)))) | → | a0#(x1) | (65) |
c0#(c0(a0(a2(x1)))) | → | a0#(c2(b0(c1(a0(x1))))) | (66) |
c0#(c0(a0(a2(x1)))) | → | a0#(c2(a0(c2(b0(c1(a0(x1))))))) | (67) |
[c0(x1)] | = |
x1 +
|
||||
[c1(x1)] | = |
x1 +
|
||||
[c2(x1)] | = |
x1 +
|
||||
[b0(x1)] | = |
x1 +
|
||||
[b2(x1)] | = |
x1 +
|
||||
[a0(x1)] | = |
x1 +
|
||||
[a1(x1)] | = |
x1 +
|
||||
[a2(x1)] | = |
x1 +
|
||||
[c0#(x1)] | = |
x1 +
|
||||
[c1#(x1)] | = |
x1 +
|
||||
[a0#(x1)] | = |
x1 +
|
||||
[a1#(x1)] | = |
x1 +
|
a2(a2(x1)) | → | a2(x1) | (13) |
a1(a2(x1)) | → | a1(x1) | (40) |
a0(a2(x1)) | → | a0(x1) | (41) |
a2(b2(x1)) | → | b2(x1) | (42) |
a2(c2(x1)) | → | c2(x1) | (43) |
a1(c2(x1)) | → | c1(x1) | (44) |
a0(c2(x1)) | → | c0(x1) | (45) |
b0(a1(a2(x1))) | → | a0(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(c0(a0(a2(x1)))) | → | a2(c2(a0(c2(b0(c1(a0(x1))))))) | (48) |
c1(c0(a0(a2(x1)))) | → | a1(c2(a0(c2(b0(c1(a0(x1))))))) | (49) |
c0(c0(a0(a2(x1)))) | → | a0(c2(a0(c2(b0(c1(a0(x1))))))) | (50) |
c2(c0(a0(c2(x1)))) | → | a2(c2(a0(c2(b0(c1(c0(x1))))))) | (51) |
c1(c0(a0(c2(x1)))) | → | a1(c2(a0(c2(b0(c1(c0(x1))))))) | (52) |
c0(c0(a0(c2(x1)))) | → | a0(c2(a0(c2(b0(c1(c0(x1))))))) | (53) |
a0#(c2(x1)) | → | c0#(x1) | (98) |
The dependency pairs are split into 2 components.
a0#(a2(x1)) | → | a0#(x1) | (99) |
[a2(x1)] | = |
x1 +
|
||||
[a0#(x1)] | = |
x1 +
|
a0#(a2(x1)) | → | a0#(x1) | (99) |
The dependency pairs are split into 0 components.
c1#(c0(a0(c2(x1)))) | → | a1#(c2(a0(c2(b0(c1(c0(x1))))))) | (74) |
a1#(c2(x1)) | → | c1#(x1) | (100) |
c1#(c0(a0(a2(x1)))) | → | a1#(c2(a0(c2(b0(c1(a0(x1))))))) | (81) |
a1#(a2(x1)) | → | a1#(x1) | (101) |
[c0(x1)] | = |
|
||||||||||||
[c1(x1)] | = |
|
||||||||||||
[c2(x1)] | = |
|
||||||||||||
[b0(x1)] | = |
|
||||||||||||
[b2(x1)] | = |
|
||||||||||||
[a0(x1)] | = |
|
||||||||||||
[a1(x1)] | = |
|
||||||||||||
[a2(x1)] | = |
|
||||||||||||
[c1#(x1)] | = |
|
||||||||||||
[a1#(x1)] | = |
|
a2(a2(x1)) | → | a2(x1) | (13) |
a1(a2(x1)) | → | a1(x1) | (40) |
a0(a2(x1)) | → | a0(x1) | (41) |
a2(b2(x1)) | → | b2(x1) | (42) |
a2(c2(x1)) | → | c2(x1) | (43) |
a1(c2(x1)) | → | c1(x1) | (44) |
a0(c2(x1)) | → | c0(x1) | (45) |
b0(a1(a2(x1))) | → | a0(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(c0(a0(a2(x1)))) | → | a2(c2(a0(c2(b0(c1(a0(x1))))))) | (48) |
c1(c0(a0(a2(x1)))) | → | a1(c2(a0(c2(b0(c1(a0(x1))))))) | (49) |
c0(c0(a0(a2(x1)))) | → | a0(c2(a0(c2(b0(c1(a0(x1))))))) | (50) |
c2(c0(a0(c2(x1)))) | → | a2(c2(a0(c2(b0(c1(c0(x1))))))) | (51) |
c1(c0(a0(c2(x1)))) | → | a1(c2(a0(c2(b0(c1(c0(x1))))))) | (52) |
c0(c0(a0(c2(x1)))) | → | a0(c2(a0(c2(b0(c1(c0(x1))))))) | (53) |
a1#(c2(x1)) | → | c1#(x1) | (100) |
[c0(x1)] | = |
x1 +
|
||||
[c1(x1)] | = |
x1 +
|
||||
[c2(x1)] | = |
x1 +
|
||||
[b0(x1)] | = |
x1 +
|
||||
[b2(x1)] | = |
x1 +
|
||||
[a0(x1)] | = |
x1 +
|
||||
[a1(x1)] | = |
x1 +
|
||||
[a2(x1)] | = |
x1 +
|
||||
[c1#(x1)] | = |
x1 +
|
||||
[a1#(x1)] | = |
x1 +
|
a2(a2(x1)) | → | a2(x1) | (13) |
a1(a2(x1)) | → | a1(x1) | (40) |
a0(a2(x1)) | → | a0(x1) | (41) |
a2(b2(x1)) | → | b2(x1) | (42) |
a2(c2(x1)) | → | c2(x1) | (43) |
a1(c2(x1)) | → | c1(x1) | (44) |
a0(c2(x1)) | → | c0(x1) | (45) |
b0(a1(a2(x1))) | → | a0(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(c0(a0(a2(x1)))) | → | a2(c2(a0(c2(b0(c1(a0(x1))))))) | (48) |
c1(c0(a0(a2(x1)))) | → | a1(c2(a0(c2(b0(c1(a0(x1))))))) | (49) |
c0(c0(a0(a2(x1)))) | → | a0(c2(a0(c2(b0(c1(a0(x1))))))) | (50) |
c2(c0(a0(c2(x1)))) | → | a2(c2(a0(c2(b0(c1(c0(x1))))))) | (51) |
c1(c0(a0(c2(x1)))) | → | a1(c2(a0(c2(b0(c1(c0(x1))))))) | (52) |
c0(c0(a0(c2(x1)))) | → | a0(c2(a0(c2(b0(c1(c0(x1))))))) | (53) |
c1#(c0(a0(c2(x1)))) | → | a1#(c2(a0(c2(b0(c1(c0(x1))))))) | (74) |
c1#(c0(a0(a2(x1)))) | → | a1#(c2(a0(c2(b0(c1(a0(x1))))))) | (81) |
The dependency pairs are split into 1 component.
a1#(a2(x1)) | → | a1#(x1) | (101) |
[a2(x1)] | = |
x1 +
|
||||
[a1#(x1)] | = |
x1 +
|
a1#(a2(x1)) | → | a1#(x1) | (101) |
The dependency pairs are split into 0 components.