The rewrite relation of the following TRS is considered.
| a(a(b(a(x1)))) | → | a(a(b(b(x1)))) | (1) |
| b(b(b(b(x1)))) | → | b(a(b(a(x1)))) | (2) |
| a(b(a(a(x1)))) | → | a(a(a(b(x1)))) | (3) |
| b(a(b(b(x1)))) | → | a(b(a(a(x1)))) | (4) |
{b(☐), a(☐)}
We obtain the transformed TRS| b(a(a(b(a(x1))))) | → | b(a(a(b(b(x1))))) | (5) |
| b(b(b(b(b(x1))))) | → | b(b(a(b(a(x1))))) | (6) |
| b(a(b(a(a(x1))))) | → | b(a(a(a(b(x1))))) | (7) |
| b(b(a(b(b(x1))))) | → | b(a(b(a(a(x1))))) | (8) |
| a(a(a(b(a(x1))))) | → | a(a(a(b(b(x1))))) | (9) |
| a(b(b(b(b(x1))))) | → | a(b(a(b(a(x1))))) | (10) |
| a(a(b(a(a(x1))))) | → | a(a(a(a(b(x1))))) | (11) |
| a(b(a(b(b(x1))))) | → | a(a(b(a(a(x1))))) | (12) |
{b(☐), a(☐)}
We obtain the transformed TRS| b(b(a(a(b(a(x1)))))) | → | b(b(a(a(b(b(x1)))))) | (13) |
| b(b(b(b(b(b(x1)))))) | → | b(b(b(a(b(a(x1)))))) | (14) |
| b(b(a(b(a(a(x1)))))) | → | b(b(a(a(a(b(x1)))))) | (15) |
| b(b(b(a(b(b(x1)))))) | → | b(b(a(b(a(a(x1)))))) | (16) |
| b(a(a(a(b(a(x1)))))) | → | b(a(a(a(b(b(x1)))))) | (17) |
| b(a(b(b(b(b(x1)))))) | → | b(a(b(a(b(a(x1)))))) | (18) |
| b(a(a(b(a(a(x1)))))) | → | b(a(a(a(a(b(x1)))))) | (19) |
| b(a(b(a(b(b(x1)))))) | → | b(a(a(b(a(a(x1)))))) | (20) |
| a(b(a(a(b(a(x1)))))) | → | a(b(a(a(b(b(x1)))))) | (21) |
| a(b(b(b(b(b(x1)))))) | → | a(b(b(a(b(a(x1)))))) | (22) |
| a(b(a(b(a(a(x1)))))) | → | a(b(a(a(a(b(x1)))))) | (23) |
| a(b(b(a(b(b(x1)))))) | → | a(b(a(b(a(a(x1)))))) | (24) |
| a(a(a(a(b(a(x1)))))) | → | a(a(a(a(b(b(x1)))))) | (25) |
| a(a(b(b(b(b(x1)))))) | → | a(a(b(a(b(a(x1)))))) | (26) |
| a(a(a(b(a(a(x1)))))) | → | a(a(a(a(a(b(x1)))))) | (27) |
| a(a(b(a(b(b(x1)))))) | → | a(a(a(b(a(a(x1)))))) | (28) |
{b(☐), a(☐)}
We obtain the transformed TRS| b(b(b(a(a(b(a(x1))))))) | → | b(b(b(a(a(b(b(x1))))))) | (29) |
| b(b(b(b(b(b(b(x1))))))) | → | b(b(b(b(a(b(a(x1))))))) | (30) |
| b(b(b(a(b(a(a(x1))))))) | → | b(b(b(a(a(a(b(x1))))))) | (31) |
| b(b(b(b(a(b(b(x1))))))) | → | b(b(b(a(b(a(a(x1))))))) | (32) |
| b(b(a(a(a(b(a(x1))))))) | → | b(b(a(a(a(b(b(x1))))))) | (33) |
| b(b(a(b(b(b(b(x1))))))) | → | b(b(a(b(a(b(a(x1))))))) | (34) |
| b(b(a(a(b(a(a(x1))))))) | → | b(b(a(a(a(a(b(x1))))))) | (35) |
| b(b(a(b(a(b(b(x1))))))) | → | b(b(a(a(b(a(a(x1))))))) | (36) |
| b(a(b(a(a(b(a(x1))))))) | → | b(a(b(a(a(b(b(x1))))))) | (37) |
| b(a(b(b(b(b(b(x1))))))) | → | b(a(b(b(a(b(a(x1))))))) | (38) |
| b(a(b(a(b(a(a(x1))))))) | → | b(a(b(a(a(a(b(x1))))))) | (39) |
| b(a(b(b(a(b(b(x1))))))) | → | b(a(b(a(b(a(a(x1))))))) | (40) |
| b(a(a(a(a(b(a(x1))))))) | → | b(a(a(a(a(b(b(x1))))))) | (41) |
| b(a(a(b(b(b(b(x1))))))) | → | b(a(a(b(a(b(a(x1))))))) | (42) |
| b(a(a(a(b(a(a(x1))))))) | → | b(a(a(a(a(a(b(x1))))))) | (43) |
| b(a(a(b(a(b(b(x1))))))) | → | b(a(a(a(b(a(a(x1))))))) | (44) |
| a(b(b(a(a(b(a(x1))))))) | → | a(b(b(a(a(b(b(x1))))))) | (45) |
| a(b(b(b(b(b(b(x1))))))) | → | a(b(b(b(a(b(a(x1))))))) | (46) |
| a(b(b(a(b(a(a(x1))))))) | → | a(b(b(a(a(a(b(x1))))))) | (47) |
| a(b(b(b(a(b(b(x1))))))) | → | a(b(b(a(b(a(a(x1))))))) | (48) |
| a(b(a(a(a(b(a(x1))))))) | → | a(b(a(a(a(b(b(x1))))))) | (49) |
| a(b(a(b(b(b(b(x1))))))) | → | a(b(a(b(a(b(a(x1))))))) | (50) |
| a(b(a(a(b(a(a(x1))))))) | → | a(b(a(a(a(a(b(x1))))))) | (51) |
| a(b(a(b(a(b(b(x1))))))) | → | a(b(a(a(b(a(a(x1))))))) | (52) |
| a(a(b(a(a(b(a(x1))))))) | → | a(a(b(a(a(b(b(x1))))))) | (53) |
| a(a(b(b(b(b(b(x1))))))) | → | a(a(b(b(a(b(a(x1))))))) | (54) |
| a(a(b(a(b(a(a(x1))))))) | → | a(a(b(a(a(a(b(x1))))))) | (55) |
| a(a(b(b(a(b(b(x1))))))) | → | a(a(b(a(b(a(a(x1))))))) | (56) |
| a(a(a(a(a(b(a(x1))))))) | → | a(a(a(a(a(b(b(x1))))))) | (57) |
| a(a(a(b(b(b(b(x1))))))) | → | a(a(a(b(a(b(a(x1))))))) | (58) |
| a(a(a(a(b(a(a(x1))))))) | → | a(a(a(a(a(a(b(x1))))))) | (59) |
| a(a(a(b(a(b(b(x1))))))) | → | a(a(a(a(b(a(a(x1))))))) | (60) |
As carrier we take the set {0,...,7}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 8):
| [b(x1)] | = | 2x1 + 0 |
| [a(x1)] | = | 2x1 + 1 |
There are 256 ruless (increase limit for explicit display).
There are 256 ruless (increase limit for explicit display).
| [b0(x1)] | = |
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| [b4(x1)] | = |
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| [b2(x1)] | = |
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| [b6(x1)] | = |
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| [b1(x1)] | = |
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| [b5(x1)] | = |
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| [b3(x1)] | = |
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| [b7(x1)] | = |
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| [a0(x1)] | = |
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| [a4(x1)] | = |
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| [a2(x1)] | = |
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| [a6(x1)] | = |
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| [a1(x1)] | = |
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| [a5(x1)] | = |
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| [a3(x1)] | = |
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| [a7(x1)] | = |
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There are 224 ruless (increase limit for explicit display).
| [b0(x1)] | = |
x1 +
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| [b4(x1)] | = |
x1 +
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| [b2(x1)] | = |
x1 +
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| [b6(x1)] | = |
x1 +
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| [b1(x1)] | = |
x1 +
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| [b5(x1)] | = |
x1 +
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| [b3(x1)] | = |
x1 +
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| [b7(x1)] | = |
x1 +
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| [a0(x1)] | = |
x1 +
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| [a4(x1)] | = |
x1 +
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| [a2(x1)] | = |
x1 +
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| [a6(x1)] | = |
x1 +
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| [a1(x1)] | = |
x1 +
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| [a5(x1)] | = |
x1 +
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| [a3(x1)] | = |
x1 +
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| [a7(x1)] | = |
x1 +
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| a7(b7(a6(a5(a3(a7(a7(x1))))))) | → | b7(b6(a4(a1(a3(a7(a7(x1))))))) | (317) |
| a3(b7(a6(a5(a3(a7(a7(x1))))))) | → | b3(b6(a4(a1(a3(a7(a7(x1))))))) | (318) |
| a1(b3(a6(a5(a3(a7(a7(x1))))))) | → | b1(b2(a4(a1(a3(a7(a7(x1))))))) | (320) |
| a0(b1(a2(a5(a3(a7(a7(x1))))))) | → | b0(b0(a0(a1(a3(a7(a7(x1))))))) | (324) |
| a7(b7(a6(a5(b3(a6(a5(x1))))))) | → | b7(b6(a4(a1(b3(a6(a5(x1))))))) | (325) |
| a3(b7(a6(a5(b3(a6(a5(x1))))))) | → | b3(b6(a4(a1(b3(a6(a5(x1))))))) | (326) |
| a1(b3(a6(a5(b3(a6(a5(x1))))))) | → | b1(b2(a4(a1(b3(a6(a5(x1))))))) | (328) |
| a0(b1(a2(a5(b3(a6(a5(x1))))))) | → | b0(b0(a0(a1(b3(a6(a5(x1))))))) | (332) |
| a7(b7(a6(a5(a3(b7(a6(x1))))))) | → | b7(b6(a4(a1(a3(b7(a6(x1))))))) | (333) |
| a3(b7(a6(a5(a3(b7(a6(x1))))))) | → | b3(b6(a4(a1(a3(b7(a6(x1))))))) | (334) |
| a1(b3(a6(a5(a3(b7(a6(x1))))))) | → | b1(b2(a4(a1(a3(b7(a6(x1))))))) | (336) |
| a0(b1(a2(a5(a3(b7(a6(x1))))))) | → | b0(b0(a0(a1(a3(b7(a6(x1))))))) | (340) |
| a7(b7(a6(a5(b3(b6(a4(x1))))))) | → | b7(b6(a4(a1(b3(b6(a4(x1))))))) | (341) |
| a3(b7(a6(a5(b3(b6(a4(x1))))))) | → | b3(b6(a4(a1(b3(b6(a4(x1))))))) | (342) |
| a1(b3(a6(a5(b3(b6(a4(x1))))))) | → | b1(b2(a4(a1(b3(b6(a4(x1))))))) | (344) |
| a0(b1(a2(a5(b3(b6(a4(x1))))))) | → | b0(b0(a0(a1(b3(b6(a4(x1))))))) | (348) |
| a7(b7(a6(a5(a3(a7(b7(x1))))))) | → | b7(b6(a4(a1(a3(a7(b7(x1))))))) | (349) |
| a3(b7(a6(a5(a3(a7(b7(x1))))))) | → | b3(b6(a4(a1(a3(a7(b7(x1))))))) | (350) |
| a1(b3(a6(a5(a3(a7(b7(x1))))))) | → | b1(b2(a4(a1(a3(a7(b7(x1))))))) | (352) |
| a0(b1(a2(a5(a3(a7(b7(x1))))))) | → | b0(b0(a0(a1(a3(a7(b7(x1))))))) | (356) |
| a7(b7(a6(a5(b3(a6(b5(x1))))))) | → | b7(b6(a4(a1(b3(a6(b5(x1))))))) | (357) |
| a3(b7(a6(a5(b3(a6(b5(x1))))))) | → | b3(b6(a4(a1(b3(a6(b5(x1))))))) | (358) |
| a1(b3(a6(a5(b3(a6(b5(x1))))))) | → | b1(b2(a4(a1(b3(a6(b5(x1))))))) | (360) |
| a0(b1(a2(a5(b3(a6(b5(x1))))))) | → | b0(b0(a0(a1(b3(a6(b5(x1))))))) | (364) |
| a7(b7(a6(a5(a3(b7(b6(x1))))))) | → | b7(b6(a4(a1(a3(b7(b6(x1))))))) | (365) |
| a3(b7(a6(a5(a3(b7(b6(x1))))))) | → | b3(b6(a4(a1(a3(b7(b6(x1))))))) | (366) |
| a1(b3(a6(a5(a3(b7(b6(x1))))))) | → | b1(b2(a4(a1(a3(b7(b6(x1))))))) | (368) |
| a0(b1(a2(a5(a3(b7(b6(x1))))))) | → | b0(b0(a0(a1(a3(b7(b6(x1))))))) | (372) |
| a7(b7(a6(a5(b3(b6(b4(x1))))))) | → | b7(b6(a4(a1(b3(b6(b4(x1))))))) | (373) |
| a3(b7(a6(a5(b3(b6(b4(x1))))))) | → | b3(b6(a4(a1(b3(b6(b4(x1))))))) | (374) |
| a1(b3(a6(a5(b3(b6(b4(x1))))))) | → | b1(b2(a4(a1(b3(b6(b4(x1))))))) | (376) |
| a0(b1(a2(a5(b3(b6(b4(x1))))))) | → | b0(b0(a0(a1(b3(b6(b4(x1))))))) | (380) |
There are no rules.
There are no rules in the TRS. Hence, it is terminating.