The rewrite relation of the following TRS is considered.
a__and(tt,X) | → | mark(X) | (1) |
a__plus(N,0) | → | mark(N) | (2) |
a__plus(N,s(M)) | → | s(a__plus(mark(N),mark(M))) | (3) |
a__x(N,0) | → | 0 | (4) |
a__x(N,s(M)) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (5) |
mark(and(X1,X2)) | → | a__and(mark(X1),X2) | (6) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (7) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (8) |
mark(tt) | → | tt | (9) |
mark(0) | → | 0 | (10) |
mark(s(X)) | → | s(mark(X)) | (11) |
a__and(X1,X2) | → | and(X1,X2) | (12) |
a__plus(X1,X2) | → | plus(X1,X2) | (13) |
a__x(X1,X2) | → | x(X1,X2) | (14) |
mark#(and(X1,X2)) | → | a__and#(mark(X1),X2) | (15) |
mark#(plus(X1,X2)) | → | mark#(X1) | (16) |
a__plus#(N,s(M)) | → | a__plus#(mark(N),mark(M)) | (17) |
a__x#(N,s(M)) | → | a__x#(mark(N),mark(M)) | (18) |
a__x#(N,s(M)) | → | mark#(M) | (19) |
a__x#(N,s(M)) | → | mark#(N) | (20) |
a__plus#(N,s(M)) | → | mark#(N) | (21) |
mark#(plus(X1,X2)) | → | mark#(X2) | (22) |
a__x#(N,s(M)) | → | mark#(N) | (20) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (23) |
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (24) |
mark#(x(X1,X2)) | → | mark#(X2) | (25) |
a__and#(tt,X) | → | mark#(X) | (26) |
mark#(and(X1,X2)) | → | mark#(X1) | (27) |
a__plus#(N,0) | → | mark#(N) | (28) |
a__x#(N,s(M)) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
a__plus#(N,s(M)) | → | mark#(M) | (30) |
mark#(s(X)) | → | mark#(X) | (31) |
mark#(x(X1,X2)) | → | mark#(X1) | (32) |
The dependency pairs are split into 1 component.
mark#(x(X1,X2)) | → | mark#(X1) | (32) |
mark#(s(X)) | → | mark#(X) | (31) |
a__plus#(N,s(M)) | → | mark#(N) | (21) |
a__plus#(N,s(M)) | → | mark#(M) | (30) |
a__x#(N,s(M)) | → | mark#(N) | (20) |
a__x#(N,s(M)) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
a__plus#(N,0) | → | mark#(N) | (28) |
mark#(and(X1,X2)) | → | mark#(X1) | (27) |
a__and#(tt,X) | → | mark#(X) | (26) |
a__x#(N,s(M)) | → | mark#(M) | (19) |
a__x#(N,s(M)) | → | a__x#(mark(N),mark(M)) | (18) |
a__plus#(N,s(M)) | → | a__plus#(mark(N),mark(M)) | (17) |
mark#(x(X1,X2)) | → | mark#(X2) | (25) |
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (24) |
mark#(plus(X1,X2)) | → | mark#(X1) | (16) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (23) |
a__x#(N,s(M)) | → | mark#(N) | (20) |
mark#(plus(X1,X2)) | → | mark#(X2) | (22) |
mark#(and(X1,X2)) | → | a__and#(mark(X1),X2) | (15) |
[a__plus(x1, x2)] | = | max(x1 + 0, x2 + 591, 0) |
[s(x1)] | = | x1 + 0 |
[and(x1, x2)] | = | max(x1 + 16911, x2 + 2, 0) |
[a__x#(x1, x2)] | = | max(x1 + 15655, x2 + 15064, 0) |
[a__x(x1, x2)] | = | max(x1 + 591, x2 + 0, 0) |
[x(x1, x2)] | = | max(x1 + 591, x2 + 0, 0) |
[a__plus#(x1, x2)] | = | max(x1 + 15064, x2 + 15655, 0) |
[mark#(x1)] | = | x1 + 15064 |
[0] | = | 553 |
[a__and#(x1, x2)] | = | max(x1 + 15067, x2 + 15065, 0) |
[mark(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 591, 0) |
[tt] | = | 42199 |
[a__and(x1, x2)] | = | max(x1 + 16911, x2 + 2, 0) |
a__x(N,0) | → | 0 | (4) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (8) |
a__and(tt,X) | → | mark(X) | (1) |
a__plus(N,s(M)) | → | s(a__plus(mark(N),mark(M))) | (3) |
a__x(N,s(M)) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (5) |
mark(0) | → | 0 | (10) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (7) |
a__x(X1,X2) | → | x(X1,X2) | (14) |
a__and(X1,X2) | → | and(X1,X2) | (12) |
mark(s(X)) | → | s(mark(X)) | (11) |
mark(tt) | → | tt | (9) |
a__plus(X1,X2) | → | plus(X1,X2) | (13) |
mark(and(X1,X2)) | → | a__and(mark(X1),X2) | (6) |
a__plus(N,0) | → | mark(N) | (2) |
mark#(x(X1,X2)) | → | mark#(X1) | (32) |
a__plus#(N,s(M)) | → | mark#(M) | (30) |
a__x#(N,s(M)) | → | mark#(N) | (20) |
mark#(and(X1,X2)) | → | mark#(X1) | (27) |
a__and#(tt,X) | → | mark#(X) | (26) |
a__x#(N,s(M)) | → | mark#(N) | (20) |
mark#(plus(X1,X2)) | → | mark#(X2) | (22) |
mark#(and(X1,X2)) | → | a__and#(mark(X1),X2) | (15) |
The dependency pairs are split into 1 component.
mark#(x(X1,X2)) | → | mark#(X2) | (25) |
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (24) |
a__plus#(N,s(M)) | → | mark#(N) | (21) |
a__plus#(N,s(M)) | → | a__plus#(mark(N),mark(M)) | (17) |
a__x#(N,s(M)) | → | mark#(M) | (19) |
a__x#(N,s(M)) | → | a__x#(mark(N),mark(M)) | (18) |
a__x#(N,s(M)) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
mark#(plus(X1,X2)) | → | mark#(X1) | (16) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (23) |
mark#(s(X)) | → | mark#(X) | (31) |
a__plus#(N,0) | → | mark#(N) | (28) |
[a__plus(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | x1 + 0 |
[and(x1, x2)] | = | x2 + 1 |
[a__x#(x1, x2)] | = | x2 + 3 |
[a__x(x1, x2)] | = | x2 + 1 |
[x(x1, x2)] | = | x2 + 1 |
[a__plus#(x1, x2)] | = | x1 + 2 |
[mark#(x1)] | = | x1 + 2 |
[0] | = | 1 |
[a__and#(x1, x2)] | = | 2 |
[mark(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + 0 |
[tt] | = | 25074 |
[a__and(x1, x2)] | = | x2 + 1 |
a__x(N,0) | → | 0 | (4) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (8) |
a__and(tt,X) | → | mark(X) | (1) |
a__plus(N,s(M)) | → | s(a__plus(mark(N),mark(M))) | (3) |
a__x(N,s(M)) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (5) |
mark(0) | → | 0 | (10) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (7) |
a__x(X1,X2) | → | x(X1,X2) | (14) |
a__and(X1,X2) | → | and(X1,X2) | (12) |
mark(s(X)) | → | s(mark(X)) | (11) |
mark(tt) | → | tt | (9) |
a__plus(X1,X2) | → | plus(X1,X2) | (13) |
mark(and(X1,X2)) | → | a__and(mark(X1),X2) | (6) |
a__plus(N,0) | → | mark(N) | (2) |
mark#(x(X1,X2)) | → | mark#(X2) | (25) |
a__x#(N,s(M)) | → | mark#(M) | (19) |
The dependency pairs are split into 1 component.
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (24) |
a__plus#(N,s(M)) | → | mark#(N) | (21) |
a__plus#(N,s(M)) | → | a__plus#(mark(N),mark(M)) | (17) |
a__x#(N,s(M)) | → | a__x#(mark(N),mark(M)) | (18) |
a__x#(N,s(M)) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
mark#(plus(X1,X2)) | → | mark#(X1) | (16) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (23) |
mark#(s(X)) | → | mark#(X) | (31) |
a__plus#(N,0) | → | mark#(N) | (28) |
π(and) | = | 2 |
π(mark) | = | 1 |
π(a__and) | = | 2 |
prec(a__plus) | = | 1 | status(a__plus) | = | [1, 2] | list-extension(a__plus) | = | Lex | ||
prec(s) | = | 0 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(a__x#) | = | 2 | status(a__x#) | = | [1, 2] | list-extension(a__x#) | = | Lex | ||
prec(a__x) | = | 2 | status(a__x) | = | [1, 2] | list-extension(a__x) | = | Lex | ||
prec(x) | = | 2 | status(x) | = | [1, 2] | list-extension(x) | = | Lex | ||
prec(a__plus#) | = | 1 | status(a__plus#) | = | [1, 2] | list-extension(a__plus#) | = | Lex | ||
prec(mark#) | = | 1 | status(mark#) | = | [1] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 3 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(a__and#) | = | 0 | status(a__and#) | = | [1, 2] | list-extension(a__and#) | = | Lex | ||
prec(plus) | = | 1 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(tt) | = | 4 | status(tt) | = | [] | list-extension(tt) | = | Lex |
[a__plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[a__x#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[a__plus#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 0 |
[a__and#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[tt] | = | 0 |
a__x(N,0) | → | 0 | (4) |
mark(x(X1,X2)) | → | a__x(mark(X1),mark(X2)) | (8) |
a__and(tt,X) | → | mark(X) | (1) |
a__plus(N,s(M)) | → | s(a__plus(mark(N),mark(M))) | (3) |
a__x(N,s(M)) | → | a__plus(a__x(mark(N),mark(M)),mark(N)) | (5) |
mark(0) | → | 0 | (10) |
mark(plus(X1,X2)) | → | a__plus(mark(X1),mark(X2)) | (7) |
a__x(X1,X2) | → | x(X1,X2) | (14) |
a__and(X1,X2) | → | and(X1,X2) | (12) |
mark(s(X)) | → | s(mark(X)) | (11) |
mark(tt) | → | tt | (9) |
a__plus(X1,X2) | → | plus(X1,X2) | (13) |
mark(and(X1,X2)) | → | a__and(mark(X1),X2) | (6) |
a__plus(N,0) | → | mark(N) | (2) |
mark#(x(X1,X2)) | → | a__x#(mark(X1),mark(X2)) | (24) |
a__plus#(N,s(M)) | → | mark#(N) | (21) |
a__plus#(N,s(M)) | → | a__plus#(mark(N),mark(M)) | (17) |
a__x#(N,s(M)) | → | a__x#(mark(N),mark(M)) | (18) |
a__x#(N,s(M)) | → | a__plus#(a__x(mark(N),mark(M)),mark(N)) | (29) |
mark#(plus(X1,X2)) | → | mark#(X1) | (16) |
mark#(plus(X1,X2)) | → | a__plus#(mark(X1),mark(X2)) | (23) |
mark#(s(X)) | → | mark#(X) | (31) |
a__plus#(N,0) | → | mark#(N) | (28) |
The dependency pairs are split into 0 components.