The rewrite relation of the following TRS is considered.
a(x1) | → | x1 | (1) |
a(b(x1)) | → | b(a(c(b(a(x1))))) | (2) |
b(x1) | → | x1 | (3) |
c(c(c(x1))) | → | x1 | (4) |
{c(☐), b(☐), a(☐)}
We obtain the transformed TRSc(a(x1)) | → | c(x1) | (5) |
c(a(b(x1))) | → | c(b(a(c(b(a(x1)))))) | (6) |
c(b(x1)) | → | c(x1) | (7) |
c(c(c(c(x1)))) | → | c(x1) | (8) |
b(a(x1)) | → | b(x1) | (9) |
b(a(b(x1))) | → | b(b(a(c(b(a(x1)))))) | (10) |
b(b(x1)) | → | b(x1) | (11) |
b(c(c(c(x1)))) | → | b(x1) | (12) |
a(a(x1)) | → | a(x1) | (13) |
a(a(b(x1))) | → | a(b(a(c(b(a(x1)))))) | (14) |
a(b(x1)) | → | a(x1) | (15) |
a(c(c(c(x1)))) | → | a(x1) | (16) |
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) | (17) |
a2(a1(x1)) | → | a1(x1) | (18) |
a2(a0(x1)) | → | a0(x1) | (19) |
b2(a2(x1)) | → | b2(x1) | (20) |
b2(a1(x1)) | → | b1(x1) | (21) |
b2(a0(x1)) | → | b0(x1) | (22) |
c2(a2(x1)) | → | c2(x1) | (23) |
c2(a1(x1)) | → | c1(x1) | (24) |
c2(a0(x1)) | → | c0(x1) | (25) |
a2(a1(b2(x1))) | → | a1(b2(a0(c1(b2(a2(x1)))))) | (26) |
a2(a1(b1(x1))) | → | a1(b2(a0(c1(b2(a1(x1)))))) | (27) |
a2(a1(b0(x1))) | → | a1(b2(a0(c1(b2(a0(x1)))))) | (28) |
b2(a1(b2(x1))) | → | b1(b2(a0(c1(b2(a2(x1)))))) | (29) |
b2(a1(b1(x1))) | → | b1(b2(a0(c1(b2(a1(x1)))))) | (30) |
b2(a1(b0(x1))) | → | b1(b2(a0(c1(b2(a0(x1)))))) | (31) |
c2(a1(b2(x1))) | → | c1(b2(a0(c1(b2(a2(x1)))))) | (32) |
c2(a1(b1(x1))) | → | c1(b2(a0(c1(b2(a1(x1)))))) | (33) |
c2(a1(b0(x1))) | → | c1(b2(a0(c1(b2(a0(x1)))))) | (34) |
a1(b2(x1)) | → | a2(x1) | (35) |
a1(b1(x1)) | → | a1(x1) | (36) |
a1(b0(x1)) | → | a0(x1) | (37) |
b1(b2(x1)) | → | b2(x1) | (38) |
b1(b1(x1)) | → | b1(x1) | (39) |
b1(b0(x1)) | → | b0(x1) | (40) |
c1(b2(x1)) | → | c2(x1) | (41) |
c1(b1(x1)) | → | c1(x1) | (42) |
c1(b0(x1)) | → | c0(x1) | (43) |
a0(c0(c0(c2(x1)))) | → | a2(x1) | (44) |
a0(c0(c0(c1(x1)))) | → | a1(x1) | (45) |
a0(c0(c0(c0(x1)))) | → | a0(x1) | (46) |
b0(c0(c0(c2(x1)))) | → | b2(x1) | (47) |
b0(c0(c0(c1(x1)))) | → | b1(x1) | (48) |
b0(c0(c0(c0(x1)))) | → | b0(x1) | (49) |
c0(c0(c0(c2(x1)))) | → | c2(x1) | (50) |
c0(c0(c0(c1(x1)))) | → | c1(x1) | (51) |
c0(c0(c0(c0(x1)))) | → | c0(x1) | (52) |
a2(a2(x1)) | → | a2(x1) | (17) |
a1(a2(x1)) | → | a1(x1) | (53) |
a0(a2(x1)) | → | a0(x1) | (54) |
a2(b2(x1)) | → | b2(x1) | (55) |
a1(b2(x1)) | → | b1(x1) | (56) |
a0(b2(x1)) | → | b0(x1) | (57) |
a2(c2(x1)) | → | c2(x1) | (58) |
a1(c2(x1)) | → | c1(x1) | (59) |
a0(c2(x1)) | → | c0(x1) | (60) |
b2(a1(a2(x1))) | → | a2(b2(c1(a0(b2(a1(x1)))))) | (61) |
b1(a1(a2(x1))) | → | a1(b2(c1(a0(b2(a1(x1)))))) | (62) |
b0(a1(a2(x1))) | → | a0(b2(c1(a0(b2(a1(x1)))))) | (63) |
b2(a1(b2(x1))) | → | a2(b2(c1(a0(b2(b1(x1)))))) | (64) |
b1(a1(b2(x1))) | → | a1(b2(c1(a0(b2(b1(x1)))))) | (65) |
b0(a1(b2(x1))) | → | a0(b2(c1(a0(b2(b1(x1)))))) | (66) |
b2(a1(c2(x1))) | → | a2(b2(c1(a0(b2(c1(x1)))))) | (67) |
b1(a1(c2(x1))) | → | a1(b2(c1(a0(b2(c1(x1)))))) | (68) |
b0(a1(c2(x1))) | → | a0(b2(c1(a0(b2(c1(x1)))))) | (69) |
b2(a1(x1)) | → | a2(x1) | (70) |
b1(a1(x1)) | → | a1(x1) | (71) |
b0(a1(x1)) | → | a0(x1) | (72) |
b2(b1(x1)) | → | b2(x1) | (73) |
b1(b1(x1)) | → | b1(x1) | (39) |
b0(b1(x1)) | → | b0(x1) | (74) |
b2(c1(x1)) | → | c2(x1) | (75) |
b1(c1(x1)) | → | c1(x1) | (76) |
b0(c1(x1)) | → | c0(x1) | (77) |
c2(c0(c0(a0(x1)))) | → | a2(x1) | (78) |
c1(c0(c0(a0(x1)))) | → | a1(x1) | (79) |
c0(c0(c0(a0(x1)))) | → | a0(x1) | (80) |
c2(c0(c0(b0(x1)))) | → | b2(x1) | (81) |
c1(c0(c0(b0(x1)))) | → | b1(x1) | (82) |
c0(c0(c0(b0(x1)))) | → | b0(x1) | (83) |
c2(c0(c0(c0(x1)))) | → | c2(x1) | (84) |
c1(c0(c0(c0(x1)))) | → | c1(x1) | (85) |
c0(c0(c0(c0(x1)))) | → | c0(x1) | (52) |
c1#(c0(c0(c0(x1)))) | → | c1#(x1) | (86) |
c1#(c0(c0(b0(x1)))) | → | b1#(x1) | (87) |
c1#(c0(c0(a0(x1)))) | → | a1#(x1) | (88) |
c2#(c0(c0(c0(x1)))) | → | c2#(x1) | (89) |
c2#(c0(c0(b0(x1)))) | → | b2#(x1) | (90) |
c2#(c0(c0(a0(x1)))) | → | a2#(x1) | (91) |
b0#(c1(x1)) | → | c0#(x1) | (92) |
b0#(b1(x1)) | → | b0#(x1) | (93) |
b0#(a1(x1)) | → | a0#(x1) | (94) |
b0#(a1(c2(x1))) | → | c1#(x1) | (95) |
b0#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (96) |
b0#(a1(c2(x1))) | → | b2#(c1(x1)) | (97) |
b0#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (98) |
b0#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (99) |
b0#(a1(c2(x1))) | → | a0#(b2(c1(a0(b2(c1(x1)))))) | (100) |
b0#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (101) |
b0#(a1(b2(x1))) | → | b1#(x1) | (102) |
b0#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (103) |
b0#(a1(b2(x1))) | → | b2#(b1(x1)) | (104) |
b0#(a1(b2(x1))) | → | a0#(b2(c1(a0(b2(b1(x1)))))) | (105) |
b0#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (106) |
b0#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (107) |
b0#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (108) |
b0#(a1(a2(x1))) | → | b2#(a1(x1)) | (109) |
b0#(a1(a2(x1))) | → | a0#(b2(c1(a0(b2(a1(x1)))))) | (110) |
b0#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (111) |
b0#(a1(a2(x1))) | → | a1#(x1) | (112) |
b1#(a1(c2(x1))) | → | c1#(x1) | (113) |
b1#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (114) |
b1#(a1(c2(x1))) | → | b2#(c1(x1)) | (115) |
b1#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (116) |
b1#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (117) |
b1#(a1(c2(x1))) | → | a1#(b2(c1(a0(b2(c1(x1)))))) | (118) |
b1#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (119) |
b1#(a1(b2(x1))) | → | b1#(x1) | (120) |
b1#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (121) |
b1#(a1(b2(x1))) | → | b2#(b1(x1)) | (122) |
b1#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (123) |
b1#(a1(b2(x1))) | → | a1#(b2(c1(a0(b2(b1(x1)))))) | (124) |
b1#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (125) |
b1#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (126) |
b1#(a1(a2(x1))) | → | b2#(a1(x1)) | (127) |
b1#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (128) |
b1#(a1(a2(x1))) | → | a1#(x1) | (129) |
b1#(a1(a2(x1))) | → | a1#(b2(c1(a0(b2(a1(x1)))))) | (130) |
b2#(c1(x1)) | → | c2#(x1) | (131) |
b2#(b1(x1)) | → | b2#(x1) | (132) |
b2#(a1(x1)) | → | a2#(x1) | (133) |
b2#(a1(c2(x1))) | → | c1#(x1) | (134) |
b2#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (135) |
b2#(a1(c2(x1))) | → | b2#(c1(x1)) | (136) |
b2#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (137) |
b2#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (138) |
b2#(a1(c2(x1))) | → | a2#(b2(c1(a0(b2(c1(x1)))))) | (139) |
b2#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (140) |
b2#(a1(b2(x1))) | → | b1#(x1) | (141) |
b2#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (142) |
b2#(a1(b2(x1))) | → | b2#(b1(x1)) | (143) |
b2#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (144) |
b2#(a1(b2(x1))) | → | a2#(b2(c1(a0(b2(b1(x1)))))) | (145) |
b2#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (146) |
b2#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (147) |
b2#(a1(a2(x1))) | → | b2#(a1(x1)) | (148) |
b2#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (149) |
b2#(a1(a2(x1))) | → | a1#(x1) | (150) |
b2#(a1(a2(x1))) | → | a2#(b2(c1(a0(b2(a1(x1)))))) | (151) |
a0#(c2(x1)) | → | c0#(x1) | (152) |
a0#(b2(x1)) | → | b0#(x1) | (153) |
a0#(a2(x1)) | → | a0#(x1) | (154) |
a1#(c2(x1)) | → | c1#(x1) | (155) |
a1#(b2(x1)) | → | b1#(x1) | (156) |
a1#(a2(x1)) | → | a1#(x1) | (157) |
[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 +
|
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[a0#(x1)] | = |
x1 +
|
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[a1#(x1)] | = |
x1 +
|
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[a2#(x1)] | = |
x1 +
|
a2(a2(x1)) | → | a2(x1) | (17) |
a1(a2(x1)) | → | a1(x1) | (53) |
a0(a2(x1)) | → | a0(x1) | (54) |
a2(b2(x1)) | → | b2(x1) | (55) |
a1(b2(x1)) | → | b1(x1) | (56) |
a0(b2(x1)) | → | b0(x1) | (57) |
a2(c2(x1)) | → | c2(x1) | (58) |
a1(c2(x1)) | → | c1(x1) | (59) |
a0(c2(x1)) | → | c0(x1) | (60) |
b2(a1(a2(x1))) | → | a2(b2(c1(a0(b2(a1(x1)))))) | (61) |
b1(a1(a2(x1))) | → | a1(b2(c1(a0(b2(a1(x1)))))) | (62) |
b0(a1(a2(x1))) | → | a0(b2(c1(a0(b2(a1(x1)))))) | (63) |
b2(a1(b2(x1))) | → | a2(b2(c1(a0(b2(b1(x1)))))) | (64) |
b1(a1(b2(x1))) | → | a1(b2(c1(a0(b2(b1(x1)))))) | (65) |
b0(a1(b2(x1))) | → | a0(b2(c1(a0(b2(b1(x1)))))) | (66) |
b2(a1(c2(x1))) | → | a2(b2(c1(a0(b2(c1(x1)))))) | (67) |
b1(a1(c2(x1))) | → | a1(b2(c1(a0(b2(c1(x1)))))) | (68) |
b0(a1(c2(x1))) | → | a0(b2(c1(a0(b2(c1(x1)))))) | (69) |
b2(a1(x1)) | → | a2(x1) | (70) |
b1(a1(x1)) | → | a1(x1) | (71) |
b0(a1(x1)) | → | a0(x1) | (72) |
b2(b1(x1)) | → | b2(x1) | (73) |
b1(b1(x1)) | → | b1(x1) | (39) |
b0(b1(x1)) | → | b0(x1) | (74) |
b2(c1(x1)) | → | c2(x1) | (75) |
b1(c1(x1)) | → | c1(x1) | (76) |
b0(c1(x1)) | → | c0(x1) | (77) |
c2(c0(c0(a0(x1)))) | → | a2(x1) | (78) |
c1(c0(c0(a0(x1)))) | → | a1(x1) | (79) |
c0(c0(c0(a0(x1)))) | → | a0(x1) | (80) |
c2(c0(c0(b0(x1)))) | → | b2(x1) | (81) |
c1(c0(c0(b0(x1)))) | → | b1(x1) | (82) |
c0(c0(c0(b0(x1)))) | → | b0(x1) | (83) |
c2(c0(c0(c0(x1)))) | → | c2(x1) | (84) |
c1(c0(c0(c0(x1)))) | → | c1(x1) | (85) |
c0(c0(c0(c0(x1)))) | → | c0(x1) | (52) |
c2#(c0(c0(a0(x1)))) | → | a2#(x1) | (91) |
b0#(c1(x1)) | → | c0#(x1) | (92) |
b2#(a1(x1)) | → | a2#(x1) | (133) |
b2#(a1(c2(x1))) | → | a2#(b2(c1(a0(b2(c1(x1)))))) | (139) |
b2#(a1(b2(x1))) | → | a2#(b2(c1(a0(b2(b1(x1)))))) | (145) |
b2#(a1(a2(x1))) | → | a2#(b2(c1(a0(b2(a1(x1)))))) | (151) |
a0#(c2(x1)) | → | c0#(x1) | (152) |
The dependency pairs are split into 1 component.
c1#(c0(c0(c0(x1)))) | → | c1#(x1) | (86) |
c1#(c0(c0(b0(x1)))) | → | b1#(x1) | (87) |
b1#(a1(c2(x1))) | → | c1#(x1) | (113) |
c1#(c0(c0(a0(x1)))) | → | a1#(x1) | (88) |
a1#(c2(x1)) | → | c1#(x1) | (155) |
a1#(b2(x1)) | → | b1#(x1) | (156) |
b1#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (114) |
b1#(a1(c2(x1))) | → | b2#(c1(x1)) | (115) |
b2#(c1(x1)) | → | c2#(x1) | (131) |
c2#(c0(c0(c0(x1)))) | → | c2#(x1) | (89) |
c2#(c0(c0(b0(x1)))) | → | b2#(x1) | (90) |
b2#(b1(x1)) | → | b2#(x1) | (132) |
b2#(a1(c2(x1))) | → | c1#(x1) | (134) |
b2#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (135) |
b2#(a1(c2(x1))) | → | b2#(c1(x1)) | (136) |
b2#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (137) |
b2#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (138) |
a0#(b2(x1)) | → | b0#(x1) | (153) |
b0#(b1(x1)) | → | b0#(x1) | (93) |
b0#(a1(x1)) | → | a0#(x1) | (94) |
a0#(a2(x1)) | → | a0#(x1) | (154) |
b0#(a1(c2(x1))) | → | c1#(x1) | (95) |
b0#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (96) |
b0#(a1(c2(x1))) | → | b2#(c1(x1)) | (97) |
b2#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (140) |
b2#(a1(b2(x1))) | → | b1#(x1) | (141) |
b1#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (116) |
b2#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (142) |
b2#(a1(b2(x1))) | → | b2#(b1(x1)) | (143) |
b2#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (144) |
b2#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (146) |
b2#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (147) |
b2#(a1(a2(x1))) | → | b2#(a1(x1)) | (148) |
b2#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (149) |
b2#(a1(a2(x1))) | → | a1#(x1) | (150) |
a1#(a2(x1)) | → | a1#(x1) | (157) |
b1#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (117) |
b1#(a1(c2(x1))) | → | a1#(b2(c1(a0(b2(c1(x1)))))) | (118) |
b1#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (119) |
b1#(a1(b2(x1))) | → | b1#(x1) | (120) |
b1#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (121) |
b1#(a1(b2(x1))) | → | b2#(b1(x1)) | (122) |
b1#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (123) |
b1#(a1(b2(x1))) | → | a1#(b2(c1(a0(b2(b1(x1)))))) | (124) |
b1#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (125) |
b1#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (126) |
b1#(a1(a2(x1))) | → | b2#(a1(x1)) | (127) |
b1#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (128) |
b1#(a1(a2(x1))) | → | a1#(x1) | (129) |
b1#(a1(a2(x1))) | → | a1#(b2(c1(a0(b2(a1(x1)))))) | (130) |
b0#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (98) |
b0#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (99) |
b0#(a1(c2(x1))) | → | a0#(b2(c1(a0(b2(c1(x1)))))) | (100) |
b0#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (101) |
b0#(a1(b2(x1))) | → | b1#(x1) | (102) |
b0#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (103) |
b0#(a1(b2(x1))) | → | b2#(b1(x1)) | (104) |
b0#(a1(b2(x1))) | → | a0#(b2(c1(a0(b2(b1(x1)))))) | (105) |
b0#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (106) |
b0#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (107) |
b0#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (108) |
b0#(a1(a2(x1))) | → | b2#(a1(x1)) | (109) |
b0#(a1(a2(x1))) | → | a0#(b2(c1(a0(b2(a1(x1)))))) | (110) |
b0#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (111) |
b0#(a1(a2(x1))) | → | a1#(x1) | (112) |
[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)] | = |
|
||||||||||||
[a0(x1)] | = |
|
||||||||||||
[a1(x1)] | = |
|
||||||||||||
[a2(x1)] | = |
|
||||||||||||
[c1#(x1)] | = |
|
||||||||||||
[c2#(x1)] | = |
|
||||||||||||
[b0#(x1)] | = |
|
||||||||||||
[b1#(x1)] | = |
|
||||||||||||
[b2#(x1)] | = |
|
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[a0#(x1)] | = |
|
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[a1#(x1)] | = |
|
a2(a2(x1)) | → | a2(x1) | (17) |
a1(a2(x1)) | → | a1(x1) | (53) |
a0(a2(x1)) | → | a0(x1) | (54) |
a2(b2(x1)) | → | b2(x1) | (55) |
a1(b2(x1)) | → | b1(x1) | (56) |
a0(b2(x1)) | → | b0(x1) | (57) |
a2(c2(x1)) | → | c2(x1) | (58) |
a1(c2(x1)) | → | c1(x1) | (59) |
a0(c2(x1)) | → | c0(x1) | (60) |
b2(a1(a2(x1))) | → | a2(b2(c1(a0(b2(a1(x1)))))) | (61) |
b1(a1(a2(x1))) | → | a1(b2(c1(a0(b2(a1(x1)))))) | (62) |
b0(a1(a2(x1))) | → | a0(b2(c1(a0(b2(a1(x1)))))) | (63) |
b2(a1(b2(x1))) | → | a2(b2(c1(a0(b2(b1(x1)))))) | (64) |
b1(a1(b2(x1))) | → | a1(b2(c1(a0(b2(b1(x1)))))) | (65) |
b0(a1(b2(x1))) | → | a0(b2(c1(a0(b2(b1(x1)))))) | (66) |
b2(a1(c2(x1))) | → | a2(b2(c1(a0(b2(c1(x1)))))) | (67) |
b1(a1(c2(x1))) | → | a1(b2(c1(a0(b2(c1(x1)))))) | (68) |
b0(a1(c2(x1))) | → | a0(b2(c1(a0(b2(c1(x1)))))) | (69) |
b2(a1(x1)) | → | a2(x1) | (70) |
b1(a1(x1)) | → | a1(x1) | (71) |
b0(a1(x1)) | → | a0(x1) | (72) |
b2(b1(x1)) | → | b2(x1) | (73) |
b1(b1(x1)) | → | b1(x1) | (39) |
b0(b1(x1)) | → | b0(x1) | (74) |
b2(c1(x1)) | → | c2(x1) | (75) |
b1(c1(x1)) | → | c1(x1) | (76) |
b0(c1(x1)) | → | c0(x1) | (77) |
c2(c0(c0(a0(x1)))) | → | a2(x1) | (78) |
c1(c0(c0(a0(x1)))) | → | a1(x1) | (79) |
c0(c0(c0(a0(x1)))) | → | a0(x1) | (80) |
c2(c0(c0(b0(x1)))) | → | b2(x1) | (81) |
c1(c0(c0(b0(x1)))) | → | b1(x1) | (82) |
c0(c0(c0(b0(x1)))) | → | b0(x1) | (83) |
c2(c0(c0(c0(x1)))) | → | c2(x1) | (84) |
c1(c0(c0(c0(x1)))) | → | c1(x1) | (85) |
c0(c0(c0(c0(x1)))) | → | c0(x1) | (52) |
c1#(c0(c0(c0(x1)))) | → | c1#(x1) | (86) |
c1#(c0(c0(b0(x1)))) | → | b1#(x1) | (87) |
b1#(a1(c2(x1))) | → | c1#(x1) | (113) |
c1#(c0(c0(a0(x1)))) | → | a1#(x1) | (88) |
a1#(c2(x1)) | → | c1#(x1) | (155) |
b1#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (114) |
b1#(a1(c2(x1))) | → | b2#(c1(x1)) | (115) |
c2#(c0(c0(c0(x1)))) | → | c2#(x1) | (89) |
c2#(c0(c0(b0(x1)))) | → | b2#(x1) | (90) |
b2#(b1(x1)) | → | b2#(x1) | (132) |
b2#(a1(c2(x1))) | → | c1#(x1) | (134) |
b2#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (135) |
b2#(a1(c2(x1))) | → | b2#(c1(x1)) | (136) |
b2#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (137) |
b2#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (138) |
b0#(b1(x1)) | → | b0#(x1) | (93) |
b0#(a1(x1)) | → | a0#(x1) | (94) |
a0#(a2(x1)) | → | a0#(x1) | (154) |
b0#(a1(c2(x1))) | → | c1#(x1) | (95) |
b0#(a1(c2(x1))) | → | c1#(a0(b2(c1(x1)))) | (96) |
b0#(a1(c2(x1))) | → | b2#(c1(x1)) | (97) |
b2#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (140) |
b2#(a1(b2(x1))) | → | b1#(x1) | (141) |
b1#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (116) |
b2#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (142) |
b2#(a1(b2(x1))) | → | b2#(b1(x1)) | (143) |
b2#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (146) |
b2#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (147) |
b2#(a1(a2(x1))) | → | b2#(a1(x1)) | (148) |
b2#(a1(a2(x1))) | → | a1#(x1) | (150) |
a1#(a2(x1)) | → | a1#(x1) | (157) |
b1#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (117) |
b1#(a1(c2(x1))) | → | a1#(b2(c1(a0(b2(c1(x1)))))) | (118) |
b1#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (119) |
b1#(a1(b2(x1))) | → | b1#(x1) | (120) |
b1#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (121) |
b1#(a1(b2(x1))) | → | b2#(b1(x1)) | (122) |
b1#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (123) |
b1#(a1(b2(x1))) | → | a1#(b2(c1(a0(b2(b1(x1)))))) | (124) |
b1#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (125) |
b1#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (126) |
b1#(a1(a2(x1))) | → | b2#(a1(x1)) | (127) |
b1#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (128) |
b1#(a1(a2(x1))) | → | a1#(x1) | (129) |
b1#(a1(a2(x1))) | → | a1#(b2(c1(a0(b2(a1(x1)))))) | (130) |
b0#(a1(c2(x1))) | → | b2#(c1(a0(b2(c1(x1))))) | (98) |
b0#(a1(c2(x1))) | → | a0#(b2(c1(x1))) | (99) |
b0#(a1(c2(x1))) | → | a0#(b2(c1(a0(b2(c1(x1)))))) | (100) |
b0#(a1(b2(x1))) | → | c1#(a0(b2(b1(x1)))) | (101) |
b0#(a1(b2(x1))) | → | b1#(x1) | (102) |
b0#(a1(b2(x1))) | → | b2#(c1(a0(b2(b1(x1))))) | (103) |
b0#(a1(b2(x1))) | → | b2#(b1(x1)) | (104) |
b0#(a1(b2(x1))) | → | a0#(b2(c1(a0(b2(b1(x1)))))) | (105) |
b0#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (106) |
b0#(a1(a2(x1))) | → | c1#(a0(b2(a1(x1)))) | (107) |
b0#(a1(a2(x1))) | → | b2#(c1(a0(b2(a1(x1))))) | (108) |
b0#(a1(a2(x1))) | → | b2#(a1(x1)) | (109) |
b0#(a1(a2(x1))) | → | a0#(b2(c1(a0(b2(a1(x1)))))) | (110) |
b0#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (111) |
b0#(a1(a2(x1))) | → | a1#(x1) | (112) |
[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 +
|
||||
[c2#(x1)] | = |
x1 +
|
||||
[b0#(x1)] | = |
x1 +
|
||||
[b1#(x1)] | = |
x1 +
|
||||
[b2#(x1)] | = |
x1 +
|
||||
[a0#(x1)] | = |
x1 +
|
||||
[a1#(x1)] | = |
x1 +
|
a2(a2(x1)) | → | a2(x1) | (17) |
a1(a2(x1)) | → | a1(x1) | (53) |
a0(a2(x1)) | → | a0(x1) | (54) |
a2(b2(x1)) | → | b2(x1) | (55) |
a1(b2(x1)) | → | b1(x1) | (56) |
a0(b2(x1)) | → | b0(x1) | (57) |
a2(c2(x1)) | → | c2(x1) | (58) |
a1(c2(x1)) | → | c1(x1) | (59) |
a0(c2(x1)) | → | c0(x1) | (60) |
b2(a1(a2(x1))) | → | a2(b2(c1(a0(b2(a1(x1)))))) | (61) |
b1(a1(a2(x1))) | → | a1(b2(c1(a0(b2(a1(x1)))))) | (62) |
b0(a1(a2(x1))) | → | a0(b2(c1(a0(b2(a1(x1)))))) | (63) |
b2(a1(b2(x1))) | → | a2(b2(c1(a0(b2(b1(x1)))))) | (64) |
b1(a1(b2(x1))) | → | a1(b2(c1(a0(b2(b1(x1)))))) | (65) |
b0(a1(b2(x1))) | → | a0(b2(c1(a0(b2(b1(x1)))))) | (66) |
b2(a1(c2(x1))) | → | a2(b2(c1(a0(b2(c1(x1)))))) | (67) |
b1(a1(c2(x1))) | → | a1(b2(c1(a0(b2(c1(x1)))))) | (68) |
b0(a1(c2(x1))) | → | a0(b2(c1(a0(b2(c1(x1)))))) | (69) |
b2(a1(x1)) | → | a2(x1) | (70) |
b1(a1(x1)) | → | a1(x1) | (71) |
b0(a1(x1)) | → | a0(x1) | (72) |
b2(b1(x1)) | → | b2(x1) | (73) |
b1(b1(x1)) | → | b1(x1) | (39) |
b0(b1(x1)) | → | b0(x1) | (74) |
b2(c1(x1)) | → | c2(x1) | (75) |
b1(c1(x1)) | → | c1(x1) | (76) |
b0(c1(x1)) | → | c0(x1) | (77) |
c2(c0(c0(a0(x1)))) | → | a2(x1) | (78) |
c1(c0(c0(a0(x1)))) | → | a1(x1) | (79) |
c0(c0(c0(a0(x1)))) | → | a0(x1) | (80) |
c2(c0(c0(b0(x1)))) | → | b2(x1) | (81) |
c1(c0(c0(b0(x1)))) | → | b1(x1) | (82) |
c0(c0(c0(b0(x1)))) | → | b0(x1) | (83) |
c2(c0(c0(c0(x1)))) | → | c2(x1) | (84) |
c1(c0(c0(c0(x1)))) | → | c1(x1) | (85) |
c0(c0(c0(c0(x1)))) | → | c0(x1) | (52) |
a1#(b2(x1)) | → | b1#(x1) | (156) |
b2#(c1(x1)) | → | c2#(x1) | (131) |
a0#(b2(x1)) | → | b0#(x1) | (153) |
b2#(a1(b2(x1))) | → | a0#(b2(b1(x1))) | (144) |
b2#(a1(a2(x1))) | → | a0#(b2(a1(x1))) | (149) |
The dependency pairs are split into 0 components.