The rewrite relation of the following TRS is considered.
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(0,cons(X,XS)) | → | mark(X) | (2) |
a__sel(s(N),cons(X,XS)) | → | a__sel(mark(N),mark(XS)) | (3) |
a__minus(X,0) | → | 0 | (4) |
a__minus(s(X),s(Y)) | → | a__minus(mark(X),mark(Y)) | (5) |
a__quot(0,s(Y)) | → | 0 | (6) |
a__quot(s(X),s(Y)) | → | s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) | (7) |
a__zWquot(XS,nil) | → | nil | (8) |
a__zWquot(nil,XS) | → | nil | (9) |
a__zWquot(cons(X,XS),cons(Y,YS)) | → | cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) | (10) |
mark(from(X)) | → | a__from(mark(X)) | (11) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
mark(minus(X1,X2)) | → | a__minus(mark(X1),mark(X2)) | (13) |
mark(quot(X1,X2)) | → | a__quot(mark(X1),mark(X2)) | (14) |
mark(zWquot(X1,X2)) | → | a__zWquot(mark(X1),mark(X2)) | (15) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (16) |
mark(s(X)) | → | s(mark(X)) | (17) |
mark(0) | → | 0 | (18) |
mark(nil) | → | nil | (19) |
a__from(X) | → | from(X) | (20) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
a__minus(X1,X2) | → | minus(X1,X2) | (22) |
a__quot(X1,X2) | → | quot(X1,X2) | (23) |
a__zWquot(X1,X2) | → | zWquot(X1,X2) | (24) |
mark#(minus(X1,X2)) | → | a__minus#(mark(X1),mark(X2)) | (25) |
a__from#(X) | → | mark#(X) | (26) |
mark#(from(X)) | → | mark#(X) | (27) |
a__quot#(s(X),s(Y)) | → | a__quot#(a__minus(mark(X),mark(Y)),s(mark(Y))) | (28) |
mark#(sel(X1,X2)) | → | mark#(X2) | (29) |
mark#(quot(X1,X2)) | → | mark#(X1) | (30) |
mark#(s(X)) | → | mark#(X) | (31) |
a__minus#(s(X),s(Y)) | → | mark#(Y) | (32) |
mark#(quot(X1,X2)) | → | mark#(X2) | (33) |
mark#(zWquot(X1,X2)) | → | mark#(X1) | (34) |
a__quot#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (35) |
mark#(zWquot(X1,X2)) | → | a__zWquot#(mark(X1),mark(X2)) | (36) |
mark#(cons(X1,X2)) | → | mark#(X1) | (37) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(Y) | (38) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (39) |
mark#(quot(X1,X2)) | → | a__quot#(mark(X1),mark(X2)) | (40) |
mark#(from(X)) | → | a__from#(mark(X)) | (41) |
a__sel#(s(N),cons(X,XS)) | → | mark#(XS) | (42) |
a__minus#(s(X),s(Y)) | → | mark#(X) | (43) |
a__sel#(s(N),cons(X,XS)) | → | mark#(N) | (44) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
mark#(zWquot(X1,X2)) | → | mark#(X2) | (46) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(X) | (47) |
a__sel#(s(N),cons(X,XS)) | → | a__sel#(mark(N),mark(XS)) | (48) |
a__minus#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (49) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
mark#(minus(X1,X2)) | → | mark#(X1) | (50) |
a__sel#(0,cons(X,XS)) | → | mark#(X) | (51) |
mark#(sel(X1,X2)) | → | mark#(X1) | (52) |
a__quot#(s(X),s(Y)) | → | mark#(X) | (53) |
mark#(minus(X1,X2)) | → | mark#(X2) | (54) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | a__quot#(mark(X),mark(Y)) | (55) |
The dependency pairs are split into 1 component.
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | a__quot#(mark(X),mark(Y)) | (55) |
mark#(cons(X1,X2)) | → | mark#(X1) | (37) |
mark#(minus(X1,X2)) | → | mark#(X2) | (54) |
mark#(zWquot(X1,X2)) | → | a__zWquot#(mark(X1),mark(X2)) | (36) |
a__quot#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (35) |
a__quot#(s(X),s(Y)) | → | mark#(X) | (53) |
mark#(zWquot(X1,X2)) | → | mark#(X1) | (34) |
mark#(quot(X1,X2)) | → | mark#(X2) | (33) |
mark#(sel(X1,X2)) | → | mark#(X1) | (52) |
a__sel#(0,cons(X,XS)) | → | mark#(X) | (51) |
a__minus#(s(X),s(Y)) | → | mark#(Y) | (32) |
mark#(minus(X1,X2)) | → | mark#(X1) | (50) |
mark#(s(X)) | → | mark#(X) | (31) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
a__minus#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (49) |
a__sel#(s(N),cons(X,XS)) | → | a__sel#(mark(N),mark(XS)) | (48) |
mark#(quot(X1,X2)) | → | mark#(X1) | (30) |
mark#(sel(X1,X2)) | → | mark#(X2) | (29) |
a__quot#(s(X),s(Y)) | → | a__quot#(a__minus(mark(X),mark(Y)),s(mark(Y))) | (28) |
mark#(zWquot(X1,X2)) | → | mark#(X2) | (46) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(X) | (47) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
mark#(from(X)) | → | mark#(X) | (27) |
a__sel#(s(N),cons(X,XS)) | → | mark#(N) | (44) |
a__minus#(s(X),s(Y)) | → | mark#(X) | (43) |
a__sel#(s(N),cons(X,XS)) | → | mark#(XS) | (42) |
mark#(from(X)) | → | a__from#(mark(X)) | (41) |
mark#(quot(X1,X2)) | → | a__quot#(mark(X1),mark(X2)) | (40) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (39) |
a__from#(X) | → | mark#(X) | (26) |
mark#(minus(X1,X2)) | → | a__minus#(mark(X1),mark(X2)) | (25) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(Y) | (38) |
[a__minus(x1, x2)] | = | 1 |
[s(x1)] | = | 12214 |
[a__zWquot#(x1, x2)] | = | 12214 |
[a__from#(x1)] | = | 12214 |
[a__quot#(x1, x2)] | = | x1 + 0 |
[minus(x1, x2)] | = | 1 |
[a__from(x1)] | = | 12214 |
[a__zWquot(x1, x2)] | = | x1 + 0 |
[zWquot(x1, x2)] | = | 0 |
[a__quot(x1, x2)] | = | 12214 |
[mark#(x1)] | = | 12214 |
[0] | = | 1 |
[quot(x1, x2)] | = | 1 |
[from(x1)] | = | 1 |
[sel(x1, x2)] | = | 1 |
[a__minus#(x1, x2)] | = | x1 + 0 |
[nil] | = | 0 |
[a__sel#(x1, x2)] | = | x2 + 0 |
[mark(x1)] | = | 12214 |
[a__sel(x1, x2)] | = | 12214 |
[cons(x1, x2)] | = | 12214 |
mark(0) | → | 0 | (18) |
a__minus(X,0) | → | 0 | (4) |
mark(zWquot(X1,X2)) | → | a__zWquot(mark(X1),mark(X2)) | (15) |
a__zWquot(XS,nil) | → | nil | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(s(N),cons(X,XS)) | → | a__sel(mark(N),mark(XS)) | (3) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (16) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
mark(nil) | → | nil | (19) |
mark(s(X)) | → | s(mark(X)) | (17) |
a__minus(X1,X2) | → | minus(X1,X2) | (22) |
a__minus(s(X),s(Y)) | → | a__minus(mark(X),mark(Y)) | (5) |
a__zWquot(cons(X,XS),cons(Y,YS)) | → | cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) | (10) |
a__quot(s(X),s(Y)) | → | s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) | (7) |
a__from(X) | → | from(X) | (20) |
mark(quot(X1,X2)) | → | a__quot(mark(X1),mark(X2)) | (14) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
a__quot(X1,X2) | → | quot(X1,X2) | (23) |
a__zWquot(X1,X2) | → | zWquot(X1,X2) | (24) |
mark(from(X)) | → | a__from(mark(X)) | (11) |
a__zWquot(nil,XS) | → | nil | (9) |
mark(minus(X1,X2)) | → | a__minus(mark(X1),mark(X2)) | (13) |
a__quot(0,s(Y)) | → | 0 | (6) |
a__sel(0,cons(X,XS)) | → | mark(X) | (2) |
a__quot#(s(X),s(Y)) | → | a__quot#(a__minus(mark(X),mark(Y)),s(mark(Y))) | (28) |
The dependency pairs are split into 1 component.
mark#(zWquot(X1,X2)) | → | mark#(X2) | (46) |
mark#(zWquot(X1,X2)) | → | mark#(X1) | (34) |
mark#(zWquot(X1,X2)) | → | a__zWquot#(mark(X1),mark(X2)) | (36) |
a__from#(X) | → | mark#(X) | (26) |
a__sel#(s(N),cons(X,XS)) | → | mark#(XS) | (42) |
a__sel#(s(N),cons(X,XS)) | → | mark#(N) | (44) |
a__sel#(s(N),cons(X,XS)) | → | a__sel#(mark(N),mark(XS)) | (48) |
mark#(cons(X1,X2)) | → | mark#(X1) | (37) |
mark#(s(X)) | → | mark#(X) | (31) |
a__minus#(s(X),s(Y)) | → | mark#(Y) | (32) |
a__minus#(s(X),s(Y)) | → | mark#(X) | (43) |
a__minus#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (49) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(Y) | (38) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(X) | (47) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | a__quot#(mark(X),mark(Y)) | (55) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
a__quot#(s(X),s(Y)) | → | mark#(X) | (53) |
a__quot#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (35) |
mark#(quot(X1,X2)) | → | mark#(X2) | (33) |
mark#(quot(X1,X2)) | → | mark#(X1) | (30) |
mark#(quot(X1,X2)) | → | a__quot#(mark(X1),mark(X2)) | (40) |
mark#(sel(X1,X2)) | → | mark#(X2) | (29) |
mark#(sel(X1,X2)) | → | mark#(X1) | (52) |
mark#(sel(X1,X2)) | → | a__sel#(mark(X1),mark(X2)) | (39) |
mark#(from(X)) | → | mark#(X) | (27) |
mark#(from(X)) | → | a__from#(mark(X)) | (41) |
mark#(minus(X1,X2)) | → | mark#(X2) | (54) |
mark#(minus(X1,X2)) | → | mark#(X1) | (50) |
mark#(minus(X1,X2)) | → | a__minus#(mark(X1),mark(X2)) | (25) |
a__sel#(0,cons(X,XS)) | → | mark#(X) | (51) |
[a__minus(x1, x2)] | = | max(x1 + 0, x2 + 2, 0) |
[s(x1)] | = | x1 + 0 |
[a__zWquot#(x1, x2)] | = | max(x1 + 46576, x2 + 31893, 0) |
[a__from#(x1)] | = | x1 + 31893 |
[a__quot#(x1, x2)] | = | max(x1 + 31894, x2 + 46575, 0) |
[minus(x1, x2)] | = | max(x1 + 0, x2 + 2, 0) |
[a__from(x1)] | = | x1 + 14682 |
[a__zWquot(x1, x2)] | = | max(x1 + 14685, x2 + 29368, 0) |
[zWquot(x1, x2)] | = | max(x1 + 14685, x2 + 29368, 0) |
[a__quot(x1, x2)] | = | max(x1 + 14684, x2 + 14687, 0) |
[mark#(x1)] | = | x1 + 31892 |
[0] | = | 14688 |
[quot(x1, x2)] | = | max(x1 + 14684, x2 + 14687, 0) |
[from(x1)] | = | x1 + 14682 |
[sel(x1, x2)] | = | max(x1 + 35660, x2 + 35661, 0) |
[a__minus#(x1, x2)] | = | max(x1 + 31892, x2 + 31893, 0) |
[nil] | = | 29369 |
[a__sel#(x1, x2)] | = | max(x1 + 67552, x2 + 52869, 0) |
[mark(x1)] | = | x1 + 0 |
[a__sel(x1, x2)] | = | max(x1 + 35660, x2 + 35661, 0) |
[cons(x1, x2)] | = | max(x1 + 14682, x2 + 0, 0) |
mark(0) | → | 0 | (18) |
a__minus(X,0) | → | 0 | (4) |
mark(zWquot(X1,X2)) | → | a__zWquot(mark(X1),mark(X2)) | (15) |
a__zWquot(XS,nil) | → | nil | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(s(N),cons(X,XS)) | → | a__sel(mark(N),mark(XS)) | (3) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (16) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
mark(nil) | → | nil | (19) |
mark(s(X)) | → | s(mark(X)) | (17) |
a__minus(X1,X2) | → | minus(X1,X2) | (22) |
a__minus(s(X),s(Y)) | → | a__minus(mark(X),mark(Y)) | (5) |
a__zWquot(cons(X,XS),cons(Y,YS)) | → | cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) | (10) |
a__quot(s(X),s(Y)) | → | s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) | (7) |
a__from(X) | → | from(X) | (20) |
mark(quot(X1,X2)) | → | a__quot(mark(X1),mark(X2)) | (14) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
a__quot(X1,X2) | → | quot(X1,X2) | (23) |
a__zWquot(X1,X2) | → | zWquot(X1,X2) | (24) |
mark(from(X)) | → | a__from(mark(X)) | (11) |
a__zWquot(nil,XS) | → | nil | (9) |
mark(minus(X1,X2)) | → | a__minus(mark(X1),mark(X2)) | (13) |
a__quot(0,s(Y)) | → | 0 | (6) |
a__sel(0,cons(X,XS)) | → | mark(X) | (2) |
mark#(zWquot(X1,X2)) | → | mark#(X2) | (46) |
mark#(zWquot(X1,X2)) | → | mark#(X1) | (34) |
mark#(zWquot(X1,X2)) | → | a__zWquot#(mark(X1),mark(X2)) | (36) |
a__from#(X) | → | mark#(X) | (26) |
a__sel#(s(N),cons(X,XS)) | → | mark#(XS) | (42) |
a__sel#(s(N),cons(X,XS)) | → | mark#(N) | (44) |
mark#(cons(X1,X2)) | → | mark#(X1) | (37) |
a__minus#(s(X),s(Y)) | → | mark#(Y) | (32) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(Y) | (38) |
a__zWquot#(cons(X,XS),cons(Y,YS)) | → | mark#(X) | (47) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
a__quot#(s(X),s(Y)) | → | mark#(Y) | (45) |
a__quot#(s(X),s(Y)) | → | mark#(X) | (53) |
a__quot#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (35) |
mark#(quot(X1,X2)) | → | mark#(X2) | (33) |
mark#(quot(X1,X2)) | → | mark#(X1) | (30) |
mark#(quot(X1,X2)) | → | a__quot#(mark(X1),mark(X2)) | (40) |
mark#(sel(X1,X2)) | → | mark#(X2) | (29) |
mark#(sel(X1,X2)) | → | mark#(X1) | (52) |
mark#(from(X)) | → | mark#(X) | (27) |
mark#(from(X)) | → | a__from#(mark(X)) | (41) |
mark#(minus(X1,X2)) | → | mark#(X2) | (54) |
a__sel#(0,cons(X,XS)) | → | mark#(X) | (51) |
The dependency pairs are split into 2 components.
mark#(s(X)) | → | mark#(X) | (31) |
a__minus#(s(X),s(Y)) | → | mark#(X) | (43) |
a__minus#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (49) |
mark#(minus(X1,X2)) | → | mark#(X1) | (50) |
mark#(minus(X1,X2)) | → | a__minus#(mark(X1),mark(X2)) | (25) |
[a__minus(x1, x2)] | = | max(x1 + 2334, x2 + 2335, 0) |
[s(x1)] | = | x1 + 0 |
[a__zWquot#(x1, x2)] | = | max(0) |
[a__from#(x1)] | = | 31893 |
[a__quot#(x1, x2)] | = | max(0) |
[minus(x1, x2)] | = | max(x1 + 2334, x2 + 2335, 0) |
[a__from(x1)] | = | x1 + 41379 |
[a__zWquot(x1, x2)] | = | max(x1 + 2336, x2 + 2336, 0) |
[zWquot(x1, x2)] | = | max(x1 + 2336, x2 + 2336, 0) |
[a__quot(x1, x2)] | = | max(x2 + 2335, 0) |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 2335 |
[quot(x1, x2)] | = | max(x2 + 2335, 0) |
[from(x1)] | = | x1 + 41379 |
[sel(x1, x2)] | = | max(x2 + 0, 0) |
[a__minus#(x1, x2)] | = | max(x1 + 2332, x2 + 2333, 0) |
[nil] | = | 2337 |
[a__sel#(x1, x2)] | = | max(0) |
[mark(x1)] | = | x1 + 0 |
[a__sel(x1, x2)] | = | max(x2 + 0, 0) |
[cons(x1, x2)] | = | max(x1 + 1, x2 + 0, 0) |
mark(0) | → | 0 | (18) |
a__minus(X,0) | → | 0 | (4) |
mark(zWquot(X1,X2)) | → | a__zWquot(mark(X1),mark(X2)) | (15) |
a__zWquot(XS,nil) | → | nil | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(s(N),cons(X,XS)) | → | a__sel(mark(N),mark(XS)) | (3) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (16) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
mark(nil) | → | nil | (19) |
mark(s(X)) | → | s(mark(X)) | (17) |
a__minus(X1,X2) | → | minus(X1,X2) | (22) |
a__minus(s(X),s(Y)) | → | a__minus(mark(X),mark(Y)) | (5) |
a__zWquot(cons(X,XS),cons(Y,YS)) | → | cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) | (10) |
a__quot(s(X),s(Y)) | → | s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) | (7) |
a__from(X) | → | from(X) | (20) |
mark(quot(X1,X2)) | → | a__quot(mark(X1),mark(X2)) | (14) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
a__quot(X1,X2) | → | quot(X1,X2) | (23) |
a__zWquot(X1,X2) | → | zWquot(X1,X2) | (24) |
mark(from(X)) | → | a__from(mark(X)) | (11) |
a__zWquot(nil,XS) | → | nil | (9) |
mark(minus(X1,X2)) | → | a__minus(mark(X1),mark(X2)) | (13) |
a__quot(0,s(Y)) | → | 0 | (6) |
a__sel(0,cons(X,XS)) | → | mark(X) | (2) |
a__minus#(s(X),s(Y)) | → | mark#(X) | (43) |
mark#(minus(X1,X2)) | → | mark#(X1) | (50) |
mark#(minus(X1,X2)) | → | a__minus#(mark(X1),mark(X2)) | (25) |
The dependency pairs are split into 2 components.
mark#(s(X)) | → | mark#(X) | (31) |
[a__minus(x1, x2)] | = | 3 |
[s(x1)] | = | x1 + 1 |
[a__zWquot#(x1, x2)] | = | 0 |
[a__from#(x1)] | = | 0 |
[a__quot#(x1, x2)] | = | 0 |
[minus(x1, x2)] | = | x2 + 4 |
[a__from(x1)] | = | 3 |
[a__zWquot(x1, x2)] | = | x1 + 1 |
[zWquot(x1, x2)] | = | x1 + x2 + 2 |
[a__quot(x1, x2)] | = | x1 + 29273 |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 4 |
[quot(x1, x2)] | = | x2 + 29274 |
[from(x1)] | = | x1 + 4 |
[sel(x1, x2)] | = | 2 |
[a__minus#(x1, x2)] | = | 0 |
[nil] | = | 3 |
[a__sel#(x1, x2)] | = | 0 |
[mark(x1)] | = | 2 |
[a__sel(x1, x2)] | = | x1 + 1 |
[cons(x1, x2)] | = | x2 + 14461 |
mark#(s(X)) | → | mark#(X) | (31) |
The dependency pairs are split into 0 components.
a__minus#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (49) |
π(mark) | = | 1 |
prec(a__minus) | = | 1 | status(a__minus) | = | [] | list-extension(a__minus) | = | Lex | ||
prec(s) | = | 1 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__zWquot#) | = | 0 | status(a__zWquot#) | = | [1] | list-extension(a__zWquot#) | = | Lex | ||
prec(a__from#) | = | 0 | status(a__from#) | = | [] | list-extension(a__from#) | = | Lex | ||
prec(a__quot#) | = | 0 | status(a__quot#) | = | [] | list-extension(a__quot#) | = | Lex | ||
prec(minus) | = | 1 | status(minus) | = | [] | list-extension(minus) | = | Lex | ||
prec(a__from) | = | 4 | status(a__from) | = | [] | list-extension(a__from) | = | Lex | ||
prec(a__zWquot) | = | 4 | status(a__zWquot) | = | [1, 2] | list-extension(a__zWquot) | = | Lex | ||
prec(zWquot) | = | 4 | status(zWquot) | = | [1, 2] | list-extension(zWquot) | = | Lex | ||
prec(a__quot) | = | 2 | status(a__quot) | = | [1] | list-extension(a__quot) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 1 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(quot) | = | 2 | status(quot) | = | [1] | list-extension(quot) | = | Lex | ||
prec(from) | = | 4 | status(from) | = | [] | list-extension(from) | = | Lex | ||
prec(sel) | = | 0 | status(sel) | = | [] | list-extension(sel) | = | Lex | ||
prec(a__minus#) | = | 1 | status(a__minus#) | = | [1] | list-extension(a__minus#) | = | Lex | ||
prec(nil) | = | 5 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(a__sel#) | = | 0 | status(a__sel#) | = | [] | list-extension(a__sel#) | = | Lex | ||
prec(a__sel) | = | 0 | status(a__sel) | = | [] | list-extension(a__sel) | = | Lex | ||
prec(cons) | = | 3 | status(cons) | = | [1] | list-extension(cons) | = | Lex |
[a__minus(x1, x2)] | = | max(0) |
[s(x1)] | = | x1 + 0 |
[a__zWquot#(x1, x2)] | = | x1 + 1 |
[a__from#(x1)] | = | 1 |
[a__quot#(x1, x2)] | = | x2 + 0 |
[minus(x1, x2)] | = | max(0) |
[a__from(x1)] | = | x1 + 29284 |
[a__zWquot(x1, x2)] | = | x1 + x2 + 29284 |
[zWquot(x1, x2)] | = | x1 + x2 + 29284 |
[a__quot(x1, x2)] | = | max(x1 + 0, 0) |
[mark#(x1)] | = | 1 |
[0] | = | 0 |
[quot(x1, x2)] | = | max(x1 + 0, 0) |
[from(x1)] | = | x1 + 29284 |
[sel(x1, x2)] | = | x2 + 29284 |
[a__minus#(x1, x2)] | = | x1 + 0 |
[nil] | = | 1 |
[a__sel#(x1, x2)] | = | x1 + 1 |
[a__sel(x1, x2)] | = | x2 + 29284 |
[cons(x1, x2)] | = | max(x1 + 29283, x2 + 0, 0) |
mark(0) | → | 0 | (18) |
a__minus(X,0) | → | 0 | (4) |
mark(zWquot(X1,X2)) | → | a__zWquot(mark(X1),mark(X2)) | (15) |
a__zWquot(XS,nil) | → | nil | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(s(N),cons(X,XS)) | → | a__sel(mark(N),mark(XS)) | (3) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (16) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
mark(nil) | → | nil | (19) |
mark(s(X)) | → | s(mark(X)) | (17) |
a__minus(X1,X2) | → | minus(X1,X2) | (22) |
a__minus(s(X),s(Y)) | → | a__minus(mark(X),mark(Y)) | (5) |
a__zWquot(cons(X,XS),cons(Y,YS)) | → | cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) | (10) |
a__quot(s(X),s(Y)) | → | s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) | (7) |
a__from(X) | → | from(X) | (20) |
mark(quot(X1,X2)) | → | a__quot(mark(X1),mark(X2)) | (14) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
a__quot(X1,X2) | → | quot(X1,X2) | (23) |
a__zWquot(X1,X2) | → | zWquot(X1,X2) | (24) |
mark(from(X)) | → | a__from(mark(X)) | (11) |
a__zWquot(nil,XS) | → | nil | (9) |
mark(minus(X1,X2)) | → | a__minus(mark(X1),mark(X2)) | (13) |
a__quot(0,s(Y)) | → | 0 | (6) |
a__sel(0,cons(X,XS)) | → | mark(X) | (2) |
a__minus#(s(X),s(Y)) | → | a__minus#(mark(X),mark(Y)) | (49) |
The dependency pairs are split into 0 components.
a__sel#(s(N),cons(X,XS)) | → | a__sel#(mark(N),mark(XS)) | (48) |
π(mark) | = | 1 |
prec(a__minus) | = | 2 | status(a__minus) | = | [] | list-extension(a__minus) | = | Lex | ||
prec(s) | = | 2 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__zWquot#) | = | 0 | status(a__zWquot#) | = | [1] | list-extension(a__zWquot#) | = | Lex | ||
prec(a__from#) | = | 0 | status(a__from#) | = | [] | list-extension(a__from#) | = | Lex | ||
prec(a__quot#) | = | 0 | status(a__quot#) | = | [] | list-extension(a__quot#) | = | Lex | ||
prec(minus) | = | 2 | status(minus) | = | [] | list-extension(minus) | = | Lex | ||
prec(a__from) | = | 5 | status(a__from) | = | [] | list-extension(a__from) | = | Lex | ||
prec(a__zWquot) | = | 5 | status(a__zWquot) | = | [1, 2] | list-extension(a__zWquot) | = | Lex | ||
prec(zWquot) | = | 5 | status(zWquot) | = | [1, 2] | list-extension(zWquot) | = | Lex | ||
prec(a__quot) | = | 3 | status(a__quot) | = | [1] | list-extension(a__quot) | = | Lex | ||
prec(mark#) | = | 0 | status(mark#) | = | [] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 2 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(quot) | = | 3 | status(quot) | = | [1] | list-extension(quot) | = | Lex | ||
prec(from) | = | 5 | status(from) | = | [] | list-extension(from) | = | Lex | ||
prec(sel) | = | 1 | status(sel) | = | [] | list-extension(sel) | = | Lex | ||
prec(a__minus#) | = | 1 | status(a__minus#) | = | [1] | list-extension(a__minus#) | = | Lex | ||
prec(nil) | = | 6 | status(nil) | = | [] | list-extension(nil) | = | Lex | ||
prec(a__sel#) | = | 0 | status(a__sel#) | = | [1] | list-extension(a__sel#) | = | Lex | ||
prec(a__sel) | = | 1 | status(a__sel) | = | [] | list-extension(a__sel) | = | Lex | ||
prec(cons) | = | 4 | status(cons) | = | [1] | list-extension(cons) | = | Lex |
[a__minus(x1, x2)] | = | max(0) |
[s(x1)] | = | x1 + 0 |
[a__zWquot#(x1, x2)] | = | x1 + 1 |
[a__from#(x1)] | = | 1 |
[a__quot#(x1, x2)] | = | x2 + 0 |
[minus(x1, x2)] | = | max(0) |
[a__from(x1)] | = | x1 + 21657 |
[a__zWquot(x1, x2)] | = | x1 + x2 + 55190 |
[zWquot(x1, x2)] | = | x1 + x2 + 55190 |
[a__quot(x1, x2)] | = | max(x1 + 0, 0) |
[mark#(x1)] | = | 1 |
[0] | = | 0 |
[quot(x1, x2)] | = | max(x1 + 0, 0) |
[from(x1)] | = | x1 + 21657 |
[sel(x1, x2)] | = | x2 + 31893 |
[a__minus#(x1, x2)] | = | x1 + 0 |
[nil] | = | 1 |
[a__sel#(x1, x2)] | = | x1 + 0 |
[a__sel(x1, x2)] | = | x2 + 31893 |
[cons(x1, x2)] | = | max(x1 + 1, x2 + 0, 0) |
mark(0) | → | 0 | (18) |
a__minus(X,0) | → | 0 | (4) |
mark(zWquot(X1,X2)) | → | a__zWquot(mark(X1),mark(X2)) | (15) |
a__zWquot(XS,nil) | → | nil | (8) |
a__from(X) | → | cons(mark(X),from(s(X))) | (1) |
a__sel(s(N),cons(X,XS)) | → | a__sel(mark(N),mark(XS)) | (3) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (16) |
a__sel(X1,X2) | → | sel(X1,X2) | (21) |
mark(nil) | → | nil | (19) |
mark(s(X)) | → | s(mark(X)) | (17) |
a__minus(X1,X2) | → | minus(X1,X2) | (22) |
a__minus(s(X),s(Y)) | → | a__minus(mark(X),mark(Y)) | (5) |
a__zWquot(cons(X,XS),cons(Y,YS)) | → | cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS)) | (10) |
a__quot(s(X),s(Y)) | → | s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))) | (7) |
a__from(X) | → | from(X) | (20) |
mark(quot(X1,X2)) | → | a__quot(mark(X1),mark(X2)) | (14) |
mark(sel(X1,X2)) | → | a__sel(mark(X1),mark(X2)) | (12) |
a__quot(X1,X2) | → | quot(X1,X2) | (23) |
a__zWquot(X1,X2) | → | zWquot(X1,X2) | (24) |
mark(from(X)) | → | a__from(mark(X)) | (11) |
a__zWquot(nil,XS) | → | nil | (9) |
mark(minus(X1,X2)) | → | a__minus(mark(X1),mark(X2)) | (13) |
a__quot(0,s(Y)) | → | 0 | (6) |
a__sel(0,cons(X,XS)) | → | mark(X) | (2) |
a__sel#(s(N),cons(X,XS)) | → | a__sel#(mark(N),mark(XS)) | (48) |
The dependency pairs are split into 0 components.