The rewrite relation of the following TRS is considered.
a(b(x1)) | → | x1 | (1) |
a(c(x1)) | → | b(c(c(a(x1)))) | (2) |
b(c(x1)) | → | a(b(x1)) | (3) |
{c(☐), b(☐), a(☐)}
We obtain the transformed TRSc(a(b(x1))) | → | c(x1) | (4) |
c(a(c(x1))) | → | c(b(c(c(a(x1))))) | (5) |
c(b(c(x1))) | → | c(a(b(x1))) | (6) |
b(a(b(x1))) | → | b(x1) | (7) |
b(a(c(x1))) | → | b(b(c(c(a(x1))))) | (8) |
b(b(c(x1))) | → | b(a(b(x1))) | (9) |
a(a(b(x1))) | → | a(x1) | (10) |
a(a(c(x1))) | → | a(b(c(c(a(x1))))) | (11) |
a(b(c(x1))) | → | a(a(b(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(a1(b2(x1))) | → | a2(x1) | (13) |
a2(a1(b1(x1))) | → | a1(x1) | (14) |
a2(a1(b0(x1))) | → | a0(x1) | (15) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b2(a1(b1(x1))) | → | b1(x1) | (17) |
b2(a1(b0(x1))) | → | b0(x1) | (18) |
c2(a1(b2(x1))) | → | c2(x1) | (19) |
c2(a1(b1(x1))) | → | c1(x1) | (20) |
c2(a1(b0(x1))) | → | c0(x1) | (21) |
a2(a0(c2(x1))) | → | a1(b0(c0(c2(a2(x1))))) | (22) |
a2(a0(c1(x1))) | → | a1(b0(c0(c2(a1(x1))))) | (23) |
a2(a0(c0(x1))) | → | a1(b0(c0(c2(a0(x1))))) | (24) |
b2(a0(c2(x1))) | → | b1(b0(c0(c2(a2(x1))))) | (25) |
b2(a0(c1(x1))) | → | b1(b0(c0(c2(a1(x1))))) | (26) |
b2(a0(c0(x1))) | → | b1(b0(c0(c2(a0(x1))))) | (27) |
c2(a0(c2(x1))) | → | c1(b0(c0(c2(a2(x1))))) | (28) |
c2(a0(c1(x1))) | → | c1(b0(c0(c2(a1(x1))))) | (29) |
c2(a0(c0(x1))) | → | c1(b0(c0(c2(a0(x1))))) | (30) |
a1(b0(c2(x1))) | → | a2(a1(b2(x1))) | (31) |
a1(b0(c1(x1))) | → | a2(a1(b1(x1))) | (32) |
a1(b0(c0(x1))) | → | a2(a1(b0(x1))) | (33) |
b1(b0(c2(x1))) | → | b2(a1(b2(x1))) | (34) |
b1(b0(c1(x1))) | → | b2(a1(b1(x1))) | (35) |
b1(b0(c0(x1))) | → | b2(a1(b0(x1))) | (36) |
c1(b0(c2(x1))) | → | c2(a1(b2(x1))) | (37) |
c1(b0(c1(x1))) | → | c2(a1(b1(x1))) | (38) |
c1(b0(c0(x1))) | → | c2(a1(b0(x1))) | (39) |
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c0#(b0(c1(x1))) | → | c2#(x1) | (66) |
c0#(b0(c1(x1))) | → | b0#(a1(c2(x1))) | (67) |
c0#(b0(b1(x1))) | → | b0#(a1(b2(x1))) | (68) |
c0#(b0(b1(x1))) | → | b2#(x1) | (69) |
c0#(b0(a1(x1))) | → | b0#(a1(a2(x1))) | (70) |
c0#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (71) |
c0#(a0(c2(x1))) | → | c1#(x1) | (72) |
c0#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (73) |
c0#(a0(c2(x1))) | → | b0#(c1(x1)) | (74) |
c0#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (75) |
c0#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (76) |
c0#(a0(b2(x1))) | → | b0#(b1(x1)) | (77) |
c0#(a0(b2(x1))) | → | b1#(x1) | (78) |
c0#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (79) |
c0#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (80) |
c0#(a0(a2(x1))) | → | b0#(a1(x1)) | (81) |
c1#(b0(c1(x1))) | → | c2#(x1) | (82) |
c1#(b0(c1(x1))) | → | b1#(a1(c2(x1))) | (83) |
c1#(b0(b1(x1))) | → | b1#(a1(b2(x1))) | (84) |
c1#(b0(b1(x1))) | → | b2#(x1) | (85) |
c1#(b0(a1(x1))) | → | b1#(a1(a2(x1))) | (86) |
c1#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (87) |
c1#(a0(c2(x1))) | → | c1#(x1) | (88) |
c1#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (89) |
c1#(a0(c2(x1))) | → | b0#(c1(x1)) | (90) |
c1#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (91) |
c1#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (92) |
c1#(a0(b2(x1))) | → | b0#(b1(x1)) | (93) |
c1#(a0(b2(x1))) | → | b1#(x1) | (94) |
c1#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (95) |
c1#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (96) |
c1#(a0(a2(x1))) | → | b0#(a1(x1)) | (97) |
c2#(b0(c1(x1))) | → | c2#(x1) | (98) |
c2#(b0(c1(x1))) | → | b2#(a1(c2(x1))) | (99) |
c2#(b0(b1(x1))) | → | b2#(x1) | (100) |
c2#(b0(b1(x1))) | → | b2#(a1(b2(x1))) | (101) |
c2#(b0(a1(x1))) | → | b2#(a1(a2(x1))) | (102) |
c2#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (103) |
c2#(a0(c2(x1))) | → | c1#(x1) | (104) |
c2#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (105) |
c2#(a0(c2(x1))) | → | b0#(c1(x1)) | (106) |
c2#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (107) |
c2#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (108) |
c2#(a0(b2(x1))) | → | b0#(b1(x1)) | (109) |
c2#(a0(b2(x1))) | → | b1#(x1) | (110) |
c2#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (111) |
c2#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (112) |
c2#(a0(a2(x1))) | → | b0#(a1(x1)) | (113) |
b0#(a1(c2(x1))) | → | c0#(x1) | (114) |
b0#(a1(b2(x1))) | → | b0#(x1) | (115) |
b1#(a1(c2(x1))) | → | c1#(x1) | (116) |
b1#(a1(b2(x1))) | → | b1#(x1) | (117) |
[c0(x1)] | = |
x1 +
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[c1(x1)] | = |
x1 +
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[c2(x1)] | = |
x1 +
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[b0(x1)] | = |
x1 +
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[b1(x1)] | = |
x1 +
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[b2(x1)] | = |
x1 +
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[a0(x1)] | = |
x1 +
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[a1(x1)] | = |
x1 +
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[a2(x1)] | = |
x1 +
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[c0#(x1)] | = |
x1 +
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[c1#(x1)] | = |
x1 +
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[c2#(x1)] | = |
x1 +
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[b0#(x1)] | = |
x1 +
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[b1#(x1)] | = |
x1 +
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[b2#(x1)] | = |
x1 +
|
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c0#(b0(b1(x1))) | → | b2#(x1) | (69) |
c1#(b0(b1(x1))) | → | b2#(x1) | (85) |
c2#(b0(c1(x1))) | → | b2#(a1(c2(x1))) | (99) |
c2#(b0(b1(x1))) | → | b2#(x1) | (100) |
c2#(b0(b1(x1))) | → | b2#(a1(b2(x1))) | (101) |
c2#(b0(a1(x1))) | → | b2#(a1(a2(x1))) | (102) |
The dependency pairs are split into 1 component.
c0#(b0(c1(x1))) | → | c2#(x1) | (66) |
c2#(b0(c1(x1))) | → | c2#(x1) | (98) |
c2#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (103) |
c0#(b0(c1(x1))) | → | b0#(a1(c2(x1))) | (67) |
b0#(a1(c2(x1))) | → | c0#(x1) | (114) |
c0#(b0(b1(x1))) | → | b0#(a1(b2(x1))) | (68) |
b0#(a1(b2(x1))) | → | b0#(x1) | (115) |
c0#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (71) |
c0#(a0(c2(x1))) | → | c1#(x1) | (72) |
c1#(b0(c1(x1))) | → | c2#(x1) | (82) |
c2#(a0(c2(x1))) | → | c1#(x1) | (104) |
c1#(b0(c1(x1))) | → | b1#(a1(c2(x1))) | (83) |
b1#(a1(c2(x1))) | → | c1#(x1) | (116) |
c1#(b0(b1(x1))) | → | b1#(a1(b2(x1))) | (84) |
b1#(a1(b2(x1))) | → | b1#(x1) | (117) |
c1#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (87) |
c0#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (73) |
c2#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (105) |
c2#(a0(c2(x1))) | → | b0#(c1(x1)) | (106) |
c2#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (107) |
c0#(a0(c2(x1))) | → | b0#(c1(x1)) | (74) |
c0#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (75) |
c0#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (76) |
c2#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (108) |
c2#(a0(b2(x1))) | → | b0#(b1(x1)) | (109) |
c2#(a0(b2(x1))) | → | b1#(x1) | (110) |
c2#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (111) |
c0#(a0(b2(x1))) | → | b0#(b1(x1)) | (77) |
c0#(a0(b2(x1))) | → | b1#(x1) | (78) |
c0#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (79) |
c0#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (80) |
c2#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (112) |
c2#(a0(a2(x1))) | → | b0#(a1(x1)) | (113) |
c0#(a0(a2(x1))) | → | b0#(a1(x1)) | (81) |
c1#(a0(c2(x1))) | → | c1#(x1) | (88) |
c1#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (89) |
c1#(a0(c2(x1))) | → | b0#(c1(x1)) | (90) |
c1#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (91) |
c1#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (92) |
c1#(a0(b2(x1))) | → | b0#(b1(x1)) | (93) |
c1#(a0(b2(x1))) | → | b1#(x1) | (94) |
c1#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (95) |
c1#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (96) |
c1#(a0(a2(x1))) | → | b0#(a1(x1)) | (97) |
[c0(x1)] | = |
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[c1(x1)] | = |
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[c2(x1)] | = |
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[b0(x1)] | = |
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[b1(x1)] | = |
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[b2(x1)] | = |
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[a0(x1)] | = |
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[a1(x1)] | = |
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[a2(x1)] | = |
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[c0#(x1)] | = |
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[c1#(x1)] | = |
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[c2#(x1)] | = |
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[b0#(x1)] | = |
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[b1#(x1)] | = |
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b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c2#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (103) |
c0#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (71) |
c0#(a0(c2(x1))) | → | c1#(x1) | (72) |
c2#(a0(c2(x1))) | → | c1#(x1) | (104) |
c1#(a0(c2(x1))) | → | c0#(b0(c1(x1))) | (87) |
c2#(a0(c2(x1))) | → | b0#(c1(x1)) | (106) |
c2#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (107) |
c0#(a0(c2(x1))) | → | b0#(c1(x1)) | (74) |
c0#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (75) |
c2#(a0(b2(x1))) | → | b0#(b1(x1)) | (109) |
c2#(a0(b2(x1))) | → | b1#(x1) | (110) |
c2#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (111) |
c0#(a0(b2(x1))) | → | b0#(b1(x1)) | (77) |
c0#(a0(b2(x1))) | → | b1#(x1) | (78) |
c0#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (79) |
c2#(a0(a2(x1))) | → | b0#(a1(x1)) | (113) |
c0#(a0(a2(x1))) | → | b0#(a1(x1)) | (81) |
c1#(a0(c2(x1))) | → | c1#(x1) | (88) |
c1#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (89) |
c1#(a0(c2(x1))) | → | b0#(c1(x1)) | (90) |
c1#(a0(b2(x1))) | → | c0#(b0(b1(x1))) | (91) |
c1#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (92) |
c1#(a0(b2(x1))) | → | b0#(b1(x1)) | (93) |
c1#(a0(b2(x1))) | → | b1#(x1) | (94) |
c1#(a0(a2(x1))) | → | c0#(b0(a1(x1))) | (95) |
c1#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (96) |
c1#(a0(a2(x1))) | → | b0#(a1(x1)) | (97) |
[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 +
|
||||
[c0#(x1)] | = |
x1 +
|
||||
[c1#(x1)] | = |
x1 +
|
||||
[c2#(x1)] | = |
x1 +
|
||||
[b0#(x1)] | = |
x1 +
|
||||
[b1#(x1)] | = |
x1 +
|
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c0#(b0(c1(x1))) | → | c2#(x1) | (66) |
c1#(b0(c1(x1))) | → | c2#(x1) | (82) |
c0#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (73) |
c0#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (76) |
c0#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (80) |
The dependency pairs are split into 3 components.
c2#(b0(c1(x1))) | → | c2#(x1) | (98) |
c2#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (105) |
c2#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (108) |
c2#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (112) |
[c0(x1)] | = |
|
||||||||||||
[c1(x1)] | = |
|
||||||||||||
[c2(x1)] | = |
|
||||||||||||
[b0(x1)] | = |
|
||||||||||||
[b1(x1)] | = |
|
||||||||||||
[b2(x1)] | = |
|
||||||||||||
[a0(x1)] | = |
|
||||||||||||
[a1(x1)] | = |
|
||||||||||||
[a2(x1)] | = |
|
||||||||||||
[c2#(x1)] | = |
|
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c2#(a0(c2(x1))) | → | c2#(c0(b0(c1(x1)))) | (105) |
c2#(a0(b2(x1))) | → | c2#(c0(b0(b1(x1)))) | (108) |
c2#(a0(a2(x1))) | → | c2#(c0(b0(a1(x1)))) | (112) |
The dependency pairs are split into 1 component.
c2#(b0(c1(x1))) | → | c2#(x1) | (98) |
[c1(x1)] | = |
x1 +
|
||||
[b0(x1)] | = |
x1 +
|
||||
[c2#(x1)] | = |
x1 +
|
c2#(b0(c1(x1))) | → | c2#(x1) | (98) |
The dependency pairs are split into 0 components.
c0#(b0(c1(x1))) | → | b0#(a1(c2(x1))) | (67) |
b0#(a1(c2(x1))) | → | c0#(x1) | (114) |
c0#(b0(b1(x1))) | → | b0#(a1(b2(x1))) | (68) |
b0#(a1(b2(x1))) | → | b0#(x1) | (115) |
[c0(x1)] | = |
|
||||||||||||
[c1(x1)] | = |
|
||||||||||||
[c2(x1)] | = |
|
||||||||||||
[b0(x1)] | = |
|
||||||||||||
[b1(x1)] | = |
|
||||||||||||
[b2(x1)] | = |
|
||||||||||||
[a0(x1)] | = |
|
||||||||||||
[a1(x1)] | = |
|
||||||||||||
[a2(x1)] | = |
|
||||||||||||
[c0#(x1)] | = |
|
||||||||||||
[b0#(x1)] | = |
|
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c0#(b0(c1(x1))) | → | b0#(a1(c2(x1))) | (67) |
The dependency pairs are split into 1 component.
b0#(a1(c2(x1))) | → | c0#(x1) | (114) |
c0#(b0(b1(x1))) | → | b0#(a1(b2(x1))) | (68) |
b0#(a1(b2(x1))) | → | b0#(x1) | (115) |
[c0(x1)] | = |
|
||||||||||||
[c1(x1)] | = |
|
||||||||||||
[c2(x1)] | = |
|
||||||||||||
[b0(x1)] | = |
|
||||||||||||
[b1(x1)] | = |
|
||||||||||||
[b2(x1)] | = |
|
||||||||||||
[a0(x1)] | = |
|
||||||||||||
[a1(x1)] | = |
|
||||||||||||
[a2(x1)] | = |
|
||||||||||||
[c0#(x1)] | = |
|
||||||||||||
[b0#(x1)] | = |
|
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
b0#(a1(c2(x1))) | → | c0#(x1) | (114) |
[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 +
|
||||
[c0#(x1)] | = |
x1 +
|
||||
[b0#(x1)] | = |
x1 +
|
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c0#(b0(b1(x1))) | → | b0#(a1(b2(x1))) | (68) |
The dependency pairs are split into 1 component.
b0#(a1(b2(x1))) | → | b0#(x1) | (115) |
[b2(x1)] | = |
x1 +
|
||||
[a1(x1)] | = |
x1 +
|
||||
[b0#(x1)] | = |
x1 +
|
b0#(a1(b2(x1))) | → | b0#(x1) | (115) |
The dependency pairs are split into 0 components.
c1#(b0(c1(x1))) | → | b1#(a1(c2(x1))) | (83) |
b1#(a1(c2(x1))) | → | c1#(x1) | (116) |
c1#(b0(b1(x1))) | → | b1#(a1(b2(x1))) | (84) |
b1#(a1(b2(x1))) | → | b1#(x1) | (117) |
[c0(x1)] | = |
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[c1(x1)] | = |
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[c2(x1)] | = |
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[b0(x1)] | = |
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[b1(x1)] | = |
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[b2(x1)] | = |
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[a0(x1)] | = |
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[a1(x1)] | = |
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[a2(x1)] | = |
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[c1#(x1)] | = |
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[b1#(x1)] | = |
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b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c1#(b0(c1(x1))) | → | b1#(a1(c2(x1))) | (83) |
The dependency pairs are split into 1 component.
b1#(a1(c2(x1))) | → | c1#(x1) | (116) |
c1#(b0(b1(x1))) | → | b1#(a1(b2(x1))) | (84) |
b1#(a1(b2(x1))) | → | b1#(x1) | (117) |
[c0(x1)] | = |
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[c1(x1)] | = |
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[c2(x1)] | = |
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[b0(x1)] | = |
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[b1(x1)] | = |
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[b2(x1)] | = |
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[a0(x1)] | = |
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[a1(x1)] | = |
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[a2(x1)] | = |
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[c1#(x1)] | = |
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[b1#(x1)] | = |
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b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
b1#(a1(c2(x1))) | → | c1#(x1) | (116) |
[c0(x1)] | = |
x1 +
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[c1(x1)] | = |
x1 +
|
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[c2(x1)] | = |
x1 +
|
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[b0(x1)] | = |
x1 +
|
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[b1(x1)] | = |
x1 +
|
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[b2(x1)] | = |
x1 +
|
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[a0(x1)] | = |
x1 +
|
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[a1(x1)] | = |
x1 +
|
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[a2(x1)] | = |
x1 +
|
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[c1#(x1)] | = |
x1 +
|
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[b1#(x1)] | = |
x1 +
|
b2(a1(a2(x1))) | → | a2(x1) | (40) |
b1(a1(a2(x1))) | → | a1(x1) | (41) |
b0(a1(a2(x1))) | → | a0(x1) | (42) |
b2(a1(b2(x1))) | → | b2(x1) | (16) |
b1(a1(b2(x1))) | → | b1(x1) | (43) |
b0(a1(b2(x1))) | → | b0(x1) | (44) |
b2(a1(c2(x1))) | → | c2(x1) | (45) |
b1(a1(c2(x1))) | → | c1(x1) | (46) |
b0(a1(c2(x1))) | → | c0(x1) | (47) |
c2(a0(a2(x1))) | → | a2(c2(c0(b0(a1(x1))))) | (48) |
c1(a0(a2(x1))) | → | a1(c2(c0(b0(a1(x1))))) | (49) |
c0(a0(a2(x1))) | → | a0(c2(c0(b0(a1(x1))))) | (50) |
c2(a0(b2(x1))) | → | a2(c2(c0(b0(b1(x1))))) | (51) |
c1(a0(b2(x1))) | → | a1(c2(c0(b0(b1(x1))))) | (52) |
c0(a0(b2(x1))) | → | a0(c2(c0(b0(b1(x1))))) | (53) |
c2(a0(c2(x1))) | → | a2(c2(c0(b0(c1(x1))))) | (54) |
c1(a0(c2(x1))) | → | a1(c2(c0(b0(c1(x1))))) | (55) |
c0(a0(c2(x1))) | → | a0(c2(c0(b0(c1(x1))))) | (56) |
c2(b0(a1(x1))) | → | b2(a1(a2(x1))) | (57) |
c1(b0(a1(x1))) | → | b1(a1(a2(x1))) | (58) |
c0(b0(a1(x1))) | → | b0(a1(a2(x1))) | (59) |
c2(b0(b1(x1))) | → | b2(a1(b2(x1))) | (60) |
c1(b0(b1(x1))) | → | b1(a1(b2(x1))) | (61) |
c0(b0(b1(x1))) | → | b0(a1(b2(x1))) | (62) |
c2(b0(c1(x1))) | → | b2(a1(c2(x1))) | (63) |
c1(b0(c1(x1))) | → | b1(a1(c2(x1))) | (64) |
c0(b0(c1(x1))) | → | b0(a1(c2(x1))) | (65) |
c1#(b0(b1(x1))) | → | b1#(a1(b2(x1))) | (84) |
The dependency pairs are split into 1 component.
b1#(a1(b2(x1))) | → | b1#(x1) | (117) |
[b2(x1)] | = |
x1 +
|
||||
[a1(x1)] | = |
x1 +
|
||||
[b1#(x1)] | = |
x1 +
|
b1#(a1(b2(x1))) | → | b1#(x1) | (117) |
The dependency pairs are split into 0 components.