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