The rewrite relation of the following TRS is considered.
| a__nats | → | a__adx(a__zeros) | (1) |
| a__zeros | → | cons(0,zeros) | (2) |
| a__incr(cons(X,Y)) | → | cons(s(X),incr(Y)) | (3) |
| a__adx(cons(X,Y)) | → | a__incr(cons(X,adx(Y))) | (4) |
| a__hd(cons(X,Y)) | → | mark(X) | (5) |
| a__tl(cons(X,Y)) | → | mark(Y) | (6) |
| mark(nats) | → | a__nats | (7) |
| mark(adx(X)) | → | a__adx(mark(X)) | (8) |
| mark(zeros) | → | a__zeros | (9) |
| mark(incr(X)) | → | a__incr(mark(X)) | (10) |
| mark(hd(X)) | → | a__hd(mark(X)) | (11) |
| mark(tl(X)) | → | a__tl(mark(X)) | (12) |
| mark(cons(X1,X2)) | → | cons(X1,X2) | (13) |
| mark(0) | → | 0 | (14) |
| mark(s(X)) | → | s(X) | (15) |
| a__nats | → | nats | (16) |
| a__adx(X) | → | adx(X) | (17) |
| a__zeros | → | zeros | (18) |
| a__incr(X) | → | incr(X) | (19) |
| a__hd(X) | → | hd(X) | (20) |
| a__tl(X) | → | tl(X) | (21) |
| mark#(zeros) | → | a__zeros# | (22) |
| mark#(tl(X)) | → | mark#(X) | (23) |
| mark#(adx(X)) | → | a__adx#(mark(X)) | (24) |
| mark#(incr(X)) | → | mark#(X) | (25) |
| a__nats# | → | a__adx#(a__zeros) | (26) |
| a__nats# | → | a__zeros# | (27) |
| mark#(adx(X)) | → | mark#(X) | (28) |
| mark#(nats) | → | a__nats# | (29) |
| a__hd#(cons(X,Y)) | → | mark#(X) | (30) |
| mark#(tl(X)) | → | a__tl#(mark(X)) | (31) |
| mark#(hd(X)) | → | a__hd#(mark(X)) | (32) |
| a__tl#(cons(X,Y)) | → | mark#(Y) | (33) |
| mark#(incr(X)) | → | a__incr#(mark(X)) | (34) |
| a__adx#(cons(X,Y)) | → | a__incr#(cons(X,adx(Y))) | (35) |
| mark#(hd(X)) | → | mark#(X) | (36) |
The dependency pairs are split into 1 component.
| mark#(hd(X)) | → | mark#(X) | (36) |
| mark#(adx(X)) | → | mark#(X) | (28) |
| a__tl#(cons(X,Y)) | → | mark#(Y) | (33) |
| mark#(hd(X)) | → | a__hd#(mark(X)) | (32) |
| mark#(incr(X)) | → | mark#(X) | (25) |
| mark#(tl(X)) | → | mark#(X) | (23) |
| mark#(tl(X)) | → | a__tl#(mark(X)) | (31) |
| a__hd#(cons(X,Y)) | → | mark#(X) | (30) |
| [incr(x1)] | = | x1 + 0 |
| [hd(x1)] | = | x1 + 70134 |
| [s(x1)] | = | 0 |
| [a__incr(x1)] | = | x1 + 0 |
| [a__tl#(x1)] | = | x1 + 0 |
| [a__nats] | = | 70415 |
| [adx(x1)] | = | x1 + 1 |
| [zeros] | = | 26391 |
| [a__hd(x1)] | = | x1 + 70134 |
| [a__adx#(x1)] | = | 0 |
| [mark#(x1)] | = | x1 + 0 |
| [0] | = | 44022 |
| [a__zeros#] | = | 0 |
| [tl(x1)] | = | x1 + 70134 |
| [a__nats#] | = | 0 |
| [mark(x1)] | = | x1 + 70133 |
| [a__adx(x1)] | = | x1 + 1 |
| [nats] | = | 282 |
| [a__hd#(x1)] | = | x1 + 0 |
| [a__incr#(x1)] | = | 0 |
| [cons(x1, x2)] | = | x1 + x2 + 1 |
| [a__tl(x1)] | = | x1 + 70134 |
| [a__zeros] | = | 70414 |
| a__zeros | → | zeros | (18) |
| a__adx(cons(X,Y)) | → | a__incr(cons(X,adx(Y))) | (4) |
| mark(s(X)) | → | s(X) | (15) |
| mark(adx(X)) | → | a__adx(mark(X)) | (8) |
| a__nats | → | a__adx(a__zeros) | (1) |
| a__incr(cons(X,Y)) | → | cons(s(X),incr(Y)) | (3) |
| a__nats | → | nats | (16) |
| a__tl(X) | → | tl(X) | (21) |
| a__incr(X) | → | incr(X) | (19) |
| a__adx(X) | → | adx(X) | (17) |
| a__hd(cons(X,Y)) | → | mark(X) | (5) |
| mark(incr(X)) | → | a__incr(mark(X)) | (10) |
| mark(nats) | → | a__nats | (7) |
| a__hd(X) | → | hd(X) | (20) |
| mark(0) | → | 0 | (14) |
| mark(tl(X)) | → | a__tl(mark(X)) | (12) |
| mark(hd(X)) | → | a__hd(mark(X)) | (11) |
| mark(zeros) | → | a__zeros | (9) |
| mark(cons(X1,X2)) | → | cons(X1,X2) | (13) |
| a__tl(cons(X,Y)) | → | mark(Y) | (6) |
| a__zeros | → | cons(0,zeros) | (2) |
| mark#(hd(X)) | → | mark#(X) | (36) |
| mark#(adx(X)) | → | mark#(X) | (28) |
| a__tl#(cons(X,Y)) | → | mark#(Y) | (33) |
| mark#(hd(X)) | → | a__hd#(mark(X)) | (32) |
| mark#(tl(X)) | → | mark#(X) | (23) |
| mark#(tl(X)) | → | a__tl#(mark(X)) | (31) |
| a__hd#(cons(X,Y)) | → | mark#(X) | (30) |
The dependency pairs are split into 1 component.
| mark#(incr(X)) | → | mark#(X) | (25) |
| [incr(x1)] | = | x1 + 1 |
| [hd(x1)] | = | x1 + 2 |
| [s(x1)] | = | x1 + 16909 |
| [a__incr(x1)] | = | 16909 |
| [a__tl#(x1)] | = | 0 |
| [a__nats] | = | 0 |
| [adx(x1)] | = | 1 |
| [zeros] | = | 16910 |
| [a__hd(x1)] | = | x1 + 1 |
| [a__adx#(x1)] | = | 0 |
| [mark#(x1)] | = | x1 + 0 |
| [0] | = | 16909 |
| [a__zeros#] | = | 0 |
| [tl(x1)] | = | 70134 |
| [a__nats#] | = | 0 |
| [mark(x1)] | = | 16908 |
| [a__adx(x1)] | = | x1 + 0 |
| [nats] | = | 282 |
| [a__hd#(x1)] | = | 0 |
| [a__incr#(x1)] | = | 0 |
| [cons(x1, x2)] | = | 16909 |
| [a__tl(x1)] | = | 16907 |
| [a__zeros] | = | 16909 |
| mark#(incr(X)) | → | mark#(X) | (25) |
The dependency pairs are split into 0 components.