The rewrite relation of the following TRS is considered.
active(fib(N)) | → | mark(sel(N,fib1(s(0),s(0)))) | (1) |
active(fib1(X,Y)) | → | mark(cons(X,fib1(Y,add(X,Y)))) | (2) |
active(add(0,X)) | → | mark(X) | (3) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (4) |
active(sel(0,cons(X,XS))) | → | mark(X) | (5) |
active(sel(s(N),cons(X,XS))) | → | mark(sel(N,XS)) | (6) |
active(fib(X)) | → | fib(active(X)) | (7) |
active(sel(X1,X2)) | → | sel(active(X1),X2) | (8) |
active(sel(X1,X2)) | → | sel(X1,active(X2)) | (9) |
active(fib1(X1,X2)) | → | fib1(active(X1),X2) | (10) |
active(fib1(X1,X2)) | → | fib1(X1,active(X2)) | (11) |
active(s(X)) | → | s(active(X)) | (12) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (13) |
active(add(X1,X2)) | → | add(active(X1),X2) | (14) |
active(add(X1,X2)) | → | add(X1,active(X2)) | (15) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
s(mark(X)) | → | mark(s(X)) | (21) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
add(mark(X1),X2) | → | mark(add(X1,X2)) | (23) |
add(X1,mark(X2)) | → | mark(add(X1,X2)) | (24) |
proper(fib(X)) | → | fib(proper(X)) | (25) |
proper(sel(X1,X2)) | → | sel(proper(X1),proper(X2)) | (26) |
proper(fib1(X1,X2)) | → | fib1(proper(X1),proper(X2)) | (27) |
proper(s(X)) | → | s(proper(X)) | (28) |
proper(0) | → | ok(0) | (29) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (30) |
proper(add(X1,X2)) | → | add(proper(X1),proper(X2)) | (31) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
s(ok(X)) | → | ok(s(X)) | (35) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
add(ok(X1),ok(X2)) | → | ok(add(X1,X2)) | (37) |
top(mark(X)) | → | top(proper(X)) | (38) |
top(ok(X)) | → | top(active(X)) | (39) |
active#(fib1(X,Y)) | → | fib1#(Y,add(X,Y)) | (40) |
proper#(fib1(X1,X2)) | → | proper#(X2) | (41) |
fib1#(X1,mark(X2)) | → | fib1#(X1,X2) | (42) |
active#(fib1(X1,X2)) | → | active#(X1) | (43) |
fib1#(mark(X1),X2) | → | fib1#(X1,X2) | (44) |
proper#(fib1(X1,X2)) | → | proper#(X1) | (45) |
proper#(fib1(X1,X2)) | → | fib1#(proper(X1),proper(X2)) | (46) |
proper#(s(X)) | → | s#(proper(X)) | (47) |
proper#(sel(X1,X2)) | → | sel#(proper(X1),proper(X2)) | (48) |
active#(fib(N)) | → | sel#(N,fib1(s(0),s(0))) | (49) |
proper#(sel(X1,X2)) | → | proper#(X1) | (50) |
active#(sel(X1,X2)) | → | active#(X1) | (51) |
active#(add(s(X),Y)) | → | s#(add(X,Y)) | (52) |
proper#(s(X)) | → | proper#(X) | (53) |
top#(mark(X)) | → | top#(proper(X)) | (54) |
active#(add(X1,X2)) | → | add#(X1,active(X2)) | (55) |
active#(fib(N)) | → | s#(0) | (56) |
fib1#(ok(X1),ok(X2)) | → | fib1#(X1,X2) | (57) |
s#(mark(X)) | → | s#(X) | (58) |
active#(fib1(X1,X2)) | → | fib1#(X1,active(X2)) | (59) |
active#(cons(X1,X2)) | → | cons#(active(X1),X2) | (60) |
active#(sel(X1,X2)) | → | sel#(X1,active(X2)) | (61) |
active#(sel(X1,X2)) | → | sel#(active(X1),X2) | (62) |
proper#(cons(X1,X2)) | → | cons#(proper(X1),proper(X2)) | (63) |
active#(add(X1,X2)) | → | active#(X1) | (64) |
fib#(ok(X)) | → | fib#(X) | (65) |
active#(sel(X1,X2)) | → | active#(X2) | (66) |
active#(fib(X)) | → | active#(X) | (67) |
active#(fib(N)) | → | s#(0) | (56) |
active#(fib1(X1,X2)) | → | active#(X2) | (68) |
active#(add(s(X),Y)) | → | add#(X,Y) | (69) |
active#(fib(X)) | → | fib#(active(X)) | (70) |
fib#(mark(X)) | → | fib#(X) | (71) |
proper#(sel(X1,X2)) | → | proper#(X2) | (72) |
proper#(cons(X1,X2)) | → | proper#(X1) | (73) |
proper#(add(X1,X2)) | → | proper#(X1) | (74) |
top#(mark(X)) | → | proper#(X) | (75) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (76) |
active#(cons(X1,X2)) | → | active#(X1) | (77) |
top#(ok(X)) | → | active#(X) | (78) |
add#(ok(X1),ok(X2)) | → | add#(X1,X2) | (79) |
sel#(mark(X1),X2) | → | sel#(X1,X2) | (80) |
proper#(fib(X)) | → | proper#(X) | (81) |
active#(add(X1,X2)) | → | add#(active(X1),X2) | (82) |
active#(fib1(X1,X2)) | → | fib1#(active(X1),X2) | (83) |
proper#(fib(X)) | → | fib#(proper(X)) | (84) |
active#(add(X1,X2)) | → | active#(X2) | (85) |
active#(s(X)) | → | s#(active(X)) | (86) |
top#(ok(X)) | → | top#(active(X)) | (87) |
proper#(add(X1,X2)) | → | add#(proper(X1),proper(X2)) | (88) |
sel#(X1,mark(X2)) | → | sel#(X1,X2) | (89) |
proper#(cons(X1,X2)) | → | proper#(X2) | (90) |
sel#(ok(X1),ok(X2)) | → | sel#(X1,X2) | (91) |
proper#(add(X1,X2)) | → | proper#(X2) | (92) |
add#(mark(X1),X2) | → | add#(X1,X2) | (93) |
active#(fib1(X,Y)) | → | add#(X,Y) | (94) |
active#(fib1(X,Y)) | → | cons#(X,fib1(Y,add(X,Y))) | (95) |
active#(fib(N)) | → | fib1#(s(0),s(0)) | (96) |
active#(sel(s(N),cons(X,XS))) | → | sel#(N,XS) | (97) |
add#(X1,mark(X2)) | → | add#(X1,X2) | (98) |
s#(ok(X)) | → | s#(X) | (99) |
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (100) |
active#(s(X)) | → | active#(X) | (101) |
The dependency pairs are split into 9 components.
top#(ok(X)) | → | top#(active(X)) | (87) |
top#(mark(X)) | → | top#(proper(X)) | (54) |
π(cons#) | = | 2 |
π(top#) | = | 1 |
π(proper) | = | 1 |
π(ok) | = | 1 |
π(active) | = | 1 |
π(active#) | = | 1 |
prec(s) | = | 4 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(top) | = | 0 | status(top) | = | [] | list-extension(top) | = | Lex | ||
prec(fib1#) | = | 0 | status(fib1#) | = | [] | list-extension(fib1#) | = | Lex | ||
prec(fib1) | = | 3 | status(fib1) | = | [2, 1] | list-extension(fib1) | = | Lex | ||
prec(fib) | = | 5 | status(fib) | = | [1] | list-extension(fib) | = | Lex | ||
prec(0) | = | 5 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(sel#) | = | 0 | status(sel#) | = | [] | list-extension(sel#) | = | Lex | ||
prec(sel) | = | 3 | status(sel) | = | [1, 2] | list-extension(sel) | = | Lex | ||
prec(s#) | = | 0 | status(s#) | = | [] | list-extension(s#) | = | Lex | ||
prec(mark) | = | 1 | status(mark) | = | [1] | list-extension(mark) | = | Lex | ||
prec(proper#) | = | 0 | status(proper#) | = | [] | list-extension(proper#) | = | Lex | ||
prec(cons) | = | 2 | status(cons) | = | [1] | list-extension(cons) | = | Lex | ||
prec(add#) | = | 0 | status(add#) | = | [1, 2] | list-extension(add#) | = | Lex | ||
prec(add) | = | 5 | status(add) | = | [1, 2] | list-extension(add) | = | Lex | ||
prec(fib#) | = | 0 | status(fib#) | = | [] | list-extension(fib#) | = | Lex |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 1 |
[fib1#(x1, x2)] | = | max(x1 + 1, 0) |
[fib1(x1, x2)] | = | max(x1 + 36413, x2 + 36413, 0) |
[fib(x1)] | = | x1 + 43294 |
[0] | = | 1 |
[sel#(x1, x2)] | = | x2 + 1 |
[sel(x1, x2)] | = | x1 + x2 + 6879 |
[s#(x1)] | = | 1 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 1 |
[cons(x1, x2)] | = | max(x1 + 36413, x2 + 0, 0) |
[add#(x1, x2)] | = | max(x1 + 1, x2 + 1, 0) |
[add(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[fib#(x1)] | = | 1 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (4) |
active(add(X1,X2)) | → | add(X1,active(X2)) | (15) |
active(sel(X1,X2)) | → | sel(active(X1),X2) | (8) |
active(fib(N)) | → | mark(sel(N,fib1(s(0),s(0)))) | (1) |
active(add(0,X)) | → | mark(X) | (3) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
s(mark(X)) | → | mark(s(X)) | (21) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
proper(sel(X1,X2)) | → | sel(proper(X1),proper(X2)) | (26) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
proper(fib1(X1,X2)) | → | fib1(proper(X1),proper(X2)) | (27) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
active(sel(0,cons(X,XS))) | → | mark(X) | (5) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
active(fib1(X1,X2)) | → | fib1(active(X1),X2) | (10) |
active(fib(X)) | → | fib(active(X)) | (7) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(fib(X)) | → | fib(proper(X)) | (25) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (30) |
active(add(X1,X2)) | → | add(active(X1),X2) | (14) |
proper(add(X1,X2)) | → | add(proper(X1),proper(X2)) | (31) |
active(s(X)) | → | s(active(X)) | (12) |
add(mark(X1),X2) | → | mark(add(X1,X2)) | (23) |
add(X1,mark(X2)) | → | mark(add(X1,X2)) | (24) |
active(fib1(X1,X2)) | → | fib1(X1,active(X2)) | (11) |
active(sel(X1,X2)) | → | sel(X1,active(X2)) | (9) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (13) |
active(sel(s(N),cons(X,XS))) | → | mark(sel(N,XS)) | (6) |
add(ok(X1),ok(X2)) | → | ok(add(X1,X2)) | (37) |
s(ok(X)) | → | ok(s(X)) | (35) |
proper(0) | → | ok(0) | (29) |
active(fib1(X,Y)) | → | mark(cons(X,fib1(Y,add(X,Y)))) | (2) |
top#(mark(X)) | → | top#(proper(X)) | (54) |
The dependency pairs are split into 1 component.
top#(ok(X)) | → | top#(active(X)) | (87) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + 0 |
[proper(x1)] | = | 3 |
[fib(x1)] | = | x1 + 0 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[cons(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x2 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
active(add(s(X),Y)) | → | mark(s(add(X,Y))) | (4) |
active(add(X1,X2)) | → | add(X1,active(X2)) | (15) |
active(sel(X1,X2)) | → | sel(active(X1),X2) | (8) |
active(fib(N)) | → | mark(sel(N,fib1(s(0),s(0)))) | (1) |
active(add(0,X)) | → | mark(X) | (3) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
s(mark(X)) | → | mark(s(X)) | (21) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
proper(sel(X1,X2)) | → | sel(proper(X1),proper(X2)) | (26) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
proper(fib1(X1,X2)) | → | fib1(proper(X1),proper(X2)) | (27) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
active(sel(0,cons(X,XS))) | → | mark(X) | (5) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
active(fib1(X1,X2)) | → | fib1(active(X1),X2) | (10) |
active(fib(X)) | → | fib(active(X)) | (7) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(fib(X)) | → | fib(proper(X)) | (25) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (30) |
active(add(X1,X2)) | → | add(active(X1),X2) | (14) |
proper(add(X1,X2)) | → | add(proper(X1),proper(X2)) | (31) |
active(s(X)) | → | s(active(X)) | (12) |
add(mark(X1),X2) | → | mark(add(X1,X2)) | (23) |
add(X1,mark(X2)) | → | mark(add(X1,X2)) | (24) |
active(fib1(X1,X2)) | → | fib1(X1,active(X2)) | (11) |
active(sel(X1,X2)) | → | sel(X1,active(X2)) | (9) |
active(cons(X1,X2)) | → | cons(active(X1),X2) | (13) |
active(sel(s(N),cons(X,XS))) | → | mark(sel(N,XS)) | (6) |
add(ok(X1),ok(X2)) | → | ok(add(X1,X2)) | (37) |
s(ok(X)) | → | ok(s(X)) | (35) |
proper(0) | → | ok(0) | (29) |
active(fib1(X,Y)) | → | mark(cons(X,fib1(Y,add(X,Y)))) | (2) |
top#(ok(X)) | → | top#(active(X)) | (87) |
The dependency pairs are split into 0 components.
active#(s(X)) | → | active#(X) | (101) |
active#(fib1(X1,X2)) | → | active#(X2) | (68) |
active#(fib(X)) | → | active#(X) | (67) |
active#(sel(X1,X2)) | → | active#(X2) | (66) |
active#(add(X1,X2)) | → | active#(X1) | (64) |
active#(add(X1,X2)) | → | active#(X2) | (85) |
active#(sel(X1,X2)) | → | active#(X1) | (51) |
active#(cons(X1,X2)) | → | active#(X1) | (77) |
active#(fib1(X1,X2)) | → | active#(X1) | (43) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 11575 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | x1 + 0 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | 621 |
[0] | = | 4447 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 32044 |
[cons(x1, x2)] | = | x1 + x2 + 32042 |
[active#(x1)] | = | x1 + 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
s(mark(X)) | → | mark(s(X)) | (21) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
proper(sel(X1,X2)) | → | sel(proper(X1),proper(X2)) | (26) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
proper(fib1(X1,X2)) | → | fib1(proper(X1),proper(X2)) | (27) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(fib(X)) | → | fib(proper(X)) | (25) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (30) |
proper(add(X1,X2)) | → | add(proper(X1),proper(X2)) | (31) |
add(mark(X1),X2) | → | mark(add(X1,X2)) | (23) |
add(X1,mark(X2)) | → | mark(add(X1,X2)) | (24) |
add(ok(X1),ok(X2)) | → | ok(add(X1,X2)) | (37) |
s(ok(X)) | → | ok(s(X)) | (35) |
proper(0) | → | ok(0) | (29) |
active#(s(X)) | → | active#(X) | (101) |
active#(fib1(X1,X2)) | → | active#(X2) | (68) |
active#(fib(X)) | → | active#(X) | (67) |
active#(sel(X1,X2)) | → | active#(X2) | (66) |
active#(add(X1,X2)) | → | active#(X1) | (64) |
active#(add(X1,X2)) | → | active#(X2) | (85) |
active#(sel(X1,X2)) | → | active#(X1) | (51) |
active#(cons(X1,X2)) | → | active#(X1) | (77) |
active#(fib1(X1,X2)) | → | active#(X1) | (43) |
The dependency pairs are split into 0 components.
proper#(cons(X1,X2)) | → | proper#(X1) | (73) |
proper#(sel(X1,X2)) | → | proper#(X2) | (72) |
proper#(add(X1,X2)) | → | proper#(X2) | (92) |
proper#(cons(X1,X2)) | → | proper#(X2) | (90) |
proper#(s(X)) | → | proper#(X) | (53) |
proper#(sel(X1,X2)) | → | proper#(X1) | (50) |
proper#(fib(X)) | → | proper#(X) | (81) |
proper#(fib1(X1,X2)) | → | proper#(X1) | (45) |
proper#(fib1(X1,X2)) | → | proper#(X2) | (41) |
proper#(add(X1,X2)) | → | proper#(X1) | (74) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | x1 + 0 |
[fib(x1)] | = | x1 + 12831 |
[ok(x1)] | = | 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 3 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | x1 + 0 |
[active(x1)] | = | 3 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + x2 + 1 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
s(mark(X)) | → | mark(s(X)) | (21) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
proper(sel(X1,X2)) | → | sel(proper(X1),proper(X2)) | (26) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
proper(fib1(X1,X2)) | → | fib1(proper(X1),proper(X2)) | (27) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
proper(s(X)) | → | s(proper(X)) | (28) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(fib(X)) | → | fib(proper(X)) | (25) |
proper(cons(X1,X2)) | → | cons(proper(X1),proper(X2)) | (30) |
proper(add(X1,X2)) | → | add(proper(X1),proper(X2)) | (31) |
add(mark(X1),X2) | → | mark(add(X1,X2)) | (23) |
add(X1,mark(X2)) | → | mark(add(X1,X2)) | (24) |
add(ok(X1),ok(X2)) | → | ok(add(X1,X2)) | (37) |
s(ok(X)) | → | ok(s(X)) | (35) |
proper(0) | → | ok(0) | (29) |
proper#(cons(X1,X2)) | → | proper#(X1) | (73) |
proper#(sel(X1,X2)) | → | proper#(X2) | (72) |
proper#(add(X1,X2)) | → | proper#(X2) | (92) |
proper#(cons(X1,X2)) | → | proper#(X2) | (90) |
proper#(s(X)) | → | proper#(X) | (53) |
proper#(sel(X1,X2)) | → | proper#(X1) | (50) |
proper#(fib(X)) | → | proper#(X) | (81) |
proper#(fib1(X1,X2)) | → | proper#(X1) | (45) |
proper#(fib1(X1,X2)) | → | proper#(X2) | (41) |
proper#(add(X1,X2)) | → | proper#(X1) | (74) |
The dependency pairs are split into 0 components.
add#(X1,mark(X2)) | → | add#(X1,X2) | (98) |
add#(mark(X1),X2) | → | add#(X1,X2) | (93) |
add#(ok(X1),ok(X2)) | → | add#(X1,X2) | (79) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 3 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | x2 + 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
add#(X1,mark(X2)) | → | add#(X1,X2) | (98) |
add#(ok(X1),ok(X2)) | → | add#(X1,X2) | (79) |
The dependency pairs are split into 1 component.
add#(mark(X1),X2) | → | add#(X1,X2) | (93) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 36457 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 36459 |
[cons(x1, x2)] | = | x1 + x2 + 36457 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | x1 + 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
add#(mark(X1),X2) | → | add#(X1,X2) | (93) |
The dependency pairs are split into 0 components.
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (100) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (76) |
[cons#(x1, x2)] | = | x2 + 0 |
[s(x1)] | = | 33309 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 42356 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 36459 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
cons#(ok(X1),ok(X2)) | → | cons#(X1,X2) | (100) |
The dependency pairs are split into 1 component.
cons#(mark(X1),X2) | → | cons#(X1,X2) | (76) |
[cons#(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 42356 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 2 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 3 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
cons#(mark(X1),X2) | → | cons#(X1,X2) | (76) |
The dependency pairs are split into 0 components.
fib#(mark(X)) | → | fib#(X) | (71) |
fib#(ok(X)) | → | fib#(X) | (65) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 3020 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 2 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 3 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | x1 + 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
fib#(mark(X)) | → | fib#(X) | (71) |
fib#(ok(X)) | → | fib#(X) | (65) |
The dependency pairs are split into 0 components.
s#(ok(X)) | → | s#(X) | (99) |
s#(mark(X)) | → | s#(X) | (58) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 1 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 3 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
s#(ok(X)) | → | s#(X) | (99) |
s#(mark(X)) | → | s#(X) | (58) |
The dependency pairs are split into 0 components.
fib1#(ok(X1),ok(X2)) | → | fib1#(X1,X2) | (57) |
fib1#(mark(X1),X2) | → | fib1#(X1,X2) | (44) |
fib1#(X1,mark(X2)) | → | fib1#(X1,X2) | (42) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | x2 + 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 3 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
fib1#(ok(X1),ok(X2)) | → | fib1#(X1,X2) | (57) |
fib1#(X1,mark(X2)) | → | fib1#(X1,X2) | (42) |
The dependency pairs are split into 1 component.
fib1#(mark(X1),X2) | → | fib1#(X1,X2) | (44) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | x1 + 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | 0 |
[sel(x1, x2)] | = | x1 + x2 + 2 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 3 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
fib1#(mark(X1),X2) | → | fib1#(X1,X2) | (44) |
The dependency pairs are split into 0 components.
sel#(ok(X1),ok(X2)) | → | sel#(X1,X2) | (91) |
sel#(X1,mark(X2)) | → | sel#(X1,X2) | (89) |
sel#(mark(X1),X2) | → | sel#(X1,X2) | (80) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 34409 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 19098 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | x1 + 0 |
[sel(x1, x2)] | = | x1 + x2 + 85326 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 85327 |
[cons(x1, x2)] | = | x1 + x2 + 50917 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
sel#(ok(X1),ok(X2)) | → | sel#(X1,X2) | (91) |
sel#(mark(X1),X2) | → | sel#(X1,X2) | (80) |
The dependency pairs are split into 1 component.
sel#(X1,mark(X2)) | → | sel#(X1,X2) | (89) |
[cons#(x1, x2)] | = | 0 |
[s(x1)] | = | 1 |
[top(x1)] | = | 0 |
[top#(x1)] | = | 0 |
[fib1#(x1, x2)] | = | 0 |
[fib1(x1, x2)] | = | x1 + x2 + 1 |
[proper(x1)] | = | 2 |
[fib(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[sel#(x1, x2)] | = | x2 + 0 |
[sel(x1, x2)] | = | x1 + x2 + 24055 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 20948 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 45003 |
[cons(x1, x2)] | = | x1 + x2 + 1 |
[active#(x1)] | = | 0 |
[add#(x1, x2)] | = | 0 |
[add(x1, x2)] | = | x1 + 0 |
[fib#(x1)] | = | 0 |
sel(X1,mark(X2)) | → | mark(sel(X1,X2)) | (18) |
fib(mark(X)) | → | mark(fib(X)) | (16) |
cons(ok(X1),ok(X2)) | → | ok(cons(X1,X2)) | (36) |
fib1(mark(X1),X2) | → | mark(fib1(X1,X2)) | (19) |
fib(ok(X)) | → | ok(fib(X)) | (32) |
sel(mark(X1),X2) | → | mark(sel(X1,X2)) | (17) |
fib1(ok(X1),ok(X2)) | → | ok(fib1(X1,X2)) | (34) |
cons(mark(X1),X2) | → | mark(cons(X1,X2)) | (22) |
sel(ok(X1),ok(X2)) | → | ok(sel(X1,X2)) | (33) |
fib1(X1,mark(X2)) | → | mark(fib1(X1,X2)) | (20) |
proper(0) | → | ok(0) | (29) |
sel#(X1,mark(X2)) | → | sel#(X1,X2) | (89) |
The dependency pairs are split into 0 components.