The rewrite relation of the following TRS is considered.
0(0(1(2(x1)))) | → | 2(1(2(x1))) | (1) |
0(3(4(2(2(1(x1)))))) | → | 2(2(5(5(3(x1))))) | (2) |
2(2(2(5(0(2(1(x1))))))) | → | 4(2(4(5(4(4(5(x1))))))) | (3) |
2(2(5(1(1(3(4(x1))))))) | → | 2(5(0(3(3(4(x1)))))) | (4) |
3(2(2(4(0(3(4(x1))))))) | → | 3(2(1(0(4(0(x1)))))) | (5) |
4(5(1(4(2(4(1(x1))))))) | → | 0(0(4(4(0(1(x1)))))) | (6) |
0(3(4(3(0(0(0(3(x1)))))))) | → | 2(2(1(1(4(2(3(x1))))))) | (7) |
0(4(4(3(4(1(0(4(x1)))))))) | → | 2(5(2(0(3(1(x1)))))) | (8) |
4(4(1(5(1(3(1(1(3(x1))))))))) | → | 3(2(2(1(3(0(0(x1))))))) | (9) |
1(4(5(3(3(1(1(1(4(3(x1)))))))))) | → | 3(0(4(0(5(0(0(3(x1)))))))) | (10) |
1(0(3(2(4(5(3(3(2(3(5(x1))))))))))) | → | 4(0(3(0(1(2(3(2(3(5(x1)))))))))) | (11) |
1(0(3(5(5(2(0(0(4(2(5(x1))))))))))) | → | 3(0(2(0(1(1(1(3(3(3(5(3(x1)))))))))))) | (12) |
3(1(5(1(2(4(5(1(4(5(2(x1))))))))))) | → | 3(2(2(2(5(0(0(3(2(x1))))))))) | (13) |
3(3(4(4(0(4(0(1(2(0(4(x1))))))))))) | → | 3(0(5(1(5(0(3(1(5(3(1(x1))))))))))) | (14) |
1(4(5(0(1(4(1(0(3(3(1(3(x1)))))))))))) | → | 0(2(2(4(5(4(3(5(0(0(x1)))))))))) | (15) |
1(5(0(5(4(3(1(3(4(4(1(4(x1)))))))))))) | → | 4(5(0(3(4(5(0(5(3(2(x1)))))))))) | (16) |
2(0(5(2(2(4(4(1(5(2(2(4(x1)))))))))))) | → | 2(3(5(3(1(0(1(0(3(4(2(4(1(x1))))))))))))) | (17) |
0(3(3(0(5(1(3(0(4(3(3(2(3(x1))))))))))))) | → | 0(5(0(1(2(3(0(2(0(2(3(x1))))))))))) | (18) |
3(3(5(4(5(5(4(2(3(1(1(0(1(x1))))))))))))) | → | 4(1(3(3(3(4(5(2(4(3(4(1(5(x1))))))))))))) | (19) |
3(5(3(0(0(1(4(5(4(2(5(1(0(x1))))))))))))) | → | 3(0(2(0(0(1(2(5(3(0(0(x1))))))))))) | (20) |
3(5(3(0(2(5(0(1(5(2(1(1(3(x1))))))))))))) | → | 3(3(3(3(5(1(3(5(0(4(0(1(5(5(x1)))))))))))))) | (21) |
0(4(0(4(1(3(4(0(2(4(0(5(0(3(x1)))))))))))))) | → | 2(3(3(3(1(0(0(2(1(5(5(5(3(x1))))))))))))) | (22) |
1(1(0(4(1(3(0(3(2(4(2(3(2(2(x1)))))))))))))) | → | 3(0(1(4(1(5(0(5(2(0(4(4(5(1(x1)))))))))))))) | (23) |
5(0(1(4(5(5(2(2(2(0(3(4(4(3(4(x1))))))))))))))) | → | 5(4(1(4(1(1(3(1(2(2(2(1(3(1(2(x1))))))))))))))) | (24) |
0(4(4(3(4(2(3(5(0(4(2(4(3(1(1(0(x1)))))))))))))))) | → | 2(5(2(1(0(5(4(0(4(3(3(2(1(3(x1)))))))))))))) | (25) |
1(3(3(0(1(2(4(1(1(4(5(5(2(3(0(0(x1)))))))))))))))) | → | 0(3(5(0(5(0(0(4(4(4(2(1(4(0(2(2(x1)))))))))))))))) | (26) |
3(1(2(1(1(1(4(4(1(0(2(5(2(1(3(3(x1)))))))))))))))) | → | 1(3(4(2(0(3(0(5(3(1(0(1(4(4(5(3(x1)))))))))))))))) | (27) |
3(3(2(5(2(3(0(5(3(1(0(2(0(1(0(4(x1)))))))))))))))) | → | 0(2(0(3(5(1(2(1(5(2(4(2(3(0(4(5(x1)))))))))))))))) | (28) |
3(3(3(5(5(4(0(2(1(0(1(0(4(3(4(3(x1)))))))))))))))) | → | 3(2(4(4(3(5(4(0(4(4(0(4(1(4(3(3(x1)))))))))))))))) | (29) |
0(5(0(2(3(3(5(1(4(5(2(5(2(0(3(4(1(2(x1)))))))))))))))))) | → | 0(3(0(2(1(4(5(3(0(5(1(1(3(5(2(0(4(2(x1)))))))))))))))))) | (30) |
1(5(5(2(3(3(1(3(4(0(4(5(1(0(2(5(2(0(x1)))))))))))))))))) | → | 2(0(3(5(3(1(0(4(5(1(1(2(1(3(4(4(1(2(5(x1))))))))))))))))))) | (31) |
3(0(3(5(1(3(4(0(1(2(3(4(5(4(4(1(1(0(x1)))))))))))))))))) | → | 0(2(0(1(1(5(0(0(4(2(3(4(5(3(3(0(x1)))))))))))))))) | (32) |
5(1(1(0(0(2(4(2(1(5(0(5(4(1(3(5(4(0(x1)))))))))))))))))) | → | 5(0(3(1(4(5(5(2(5(1(5(1(4(3(5(5(4(x1))))))))))))))))) | (33) |
1(0(1(0(4(4(1(1(2(1(2(1(4(0(4(2(1(2(5(x1))))))))))))))))))) | → | 0(2(4(4(5(4(1(1(1(3(5(4(0(4(5(2(1(3(3(3(x1)))))))))))))))))))) | (34) |
1(5(5(4(1(5(2(3(0(3(3(2(4(5(3(4(1(1(4(x1))))))))))))))))))) | → | 4(4(0(4(4(0(0(5(5(0(5(4(0(3(3(0(1(1(4(x1))))))))))))))))))) | (35) |
2(2(3(5(1(5(4(0(0(1(4(0(1(3(5(0(3(5(1(x1))))))))))))))))))) | → | 2(1(5(0(2(1(4(4(3(1(3(5(0(4(3(1(2(x1))))))))))))))))) | (36) |
3(5(4(3(1(5(0(1(4(5(0(5(2(1(5(2(3(2(2(x1))))))))))))))))))) | → | 3(4(2(4(1(4(3(4(0(1(2(2(0(0(2(2(5(2(x1)))))))))))))))))) | (37) |
4(2(2(4(0(5(5(0(5(3(2(5(3(1(3(2(3(4(4(x1))))))))))))))))))) | → | 2(4(5(1(4(2(1(3(2(0(1(5(4(4(4(5(2(4(x1)))))))))))))))))) | (38) |
1(4(1(1(5(0(1(4(4(1(2(0(5(1(0(0(4(5(1(0(1(x1))))))))))))))))))))) | → | 0(4(3(5(3(4(2(4(2(4(1(0(2(4(4(1(3(4(4(4(1(x1))))))))))))))))))))) | (39) |
4(0(3(0(3(4(2(2(1(3(5(4(4(5(3(1(2(0(1(4(1(x1))))))))))))))))))))) | → | 2(1(0(2(5(0(0(2(0(3(3(0(5(0(2(1(3(1(x1)))))))))))))))))) | (40) |
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 240 ruless (increase limit for explicit display).
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 1440 ruless (increase limit for explicit display).
As carrier we take the set {0,...,35}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 36):
[5(x1)] | = | 6x1 + 0 |
[4(x1)] | = | 6x1 + 1 |
[3(x1)] | = | 6x1 + 2 |
[2(x1)] | = | 6x1 + 3 |
[1(x1)] | = | 6x1 + 4 |
[0(x1)] | = | 6x1 + 5 |
There are 51840 ruless (increase limit for explicit display).
[50(x1)] | = |
x1 +
|
||||
[56(x1)] | = |
x1 +
|
||||
[512(x1)] | = |
x1 +
|
||||
[518(x1)] | = |
x1 +
|
||||
[524(x1)] | = |
x1 +
|
||||
[530(x1)] | = |
x1 +
|
||||
[51(x1)] | = |
x1 +
|
||||
[57(x1)] | = |
x1 +
|
||||
[513(x1)] | = |
x1 +
|
||||
[519(x1)] | = |
x1 +
|
||||
[525(x1)] | = |
x1 +
|
||||
[531(x1)] | = |
x1 +
|
||||
[52(x1)] | = |
x1 +
|
||||
[58(x1)] | = |
x1 +
|
||||
[514(x1)] | = |
x1 +
|
||||
[520(x1)] | = |
x1 +
|
||||
[526(x1)] | = |
x1 +
|
||||
[532(x1)] | = |
x1 +
|
||||
[53(x1)] | = |
x1 +
|
||||
[59(x1)] | = |
x1 +
|
||||
[515(x1)] | = |
x1 +
|
||||
[521(x1)] | = |
x1 +
|
||||
[527(x1)] | = |
x1 +
|
||||
[533(x1)] | = |
x1 +
|
||||
[54(x1)] | = |
x1 +
|
||||
[510(x1)] | = |
x1 +
|
||||
[516(x1)] | = |
x1 +
|
||||
[522(x1)] | = |
x1 +
|
||||
[528(x1)] | = |
x1 +
|
||||
[534(x1)] | = |
x1 +
|
||||
[55(x1)] | = |
x1 +
|
||||
[511(x1)] | = |
x1 +
|
||||
[517(x1)] | = |
x1 +
|
||||
[523(x1)] | = |
x1 +
|
||||
[529(x1)] | = |
x1 +
|
||||
[535(x1)] | = |
x1 +
|
||||
[40(x1)] | = |
x1 +
|
||||
[46(x1)] | = |
x1 +
|
||||
[412(x1)] | = |
x1 +
|
||||
[418(x1)] | = |
x1 +
|
||||
[424(x1)] | = |
x1 +
|
||||
[430(x1)] | = |
x1 +
|
||||
[41(x1)] | = |
x1 +
|
||||
[47(x1)] | = |
x1 +
|
||||
[413(x1)] | = |
x1 +
|
||||
[419(x1)] | = |
x1 +
|
||||
[425(x1)] | = |
x1 +
|
||||
[431(x1)] | = |
x1 +
|
||||
[42(x1)] | = |
x1 +
|
||||
[48(x1)] | = |
x1 +
|
||||
[414(x1)] | = |
x1 +
|
||||
[420(x1)] | = |
x1 +
|
||||
[426(x1)] | = |
x1 +
|
||||
[432(x1)] | = |
x1 +
|
||||
[43(x1)] | = |
x1 +
|
||||
[49(x1)] | = |
x1 +
|
||||
[415(x1)] | = |
x1 +
|
||||
[421(x1)] | = |
x1 +
|
||||
[427(x1)] | = |
x1 +
|
||||
[433(x1)] | = |
x1 +
|
||||
[44(x1)] | = |
x1 +
|
||||
[410(x1)] | = |
x1 +
|
||||
[416(x1)] | = |
x1 +
|
||||
[422(x1)] | = |
x1 +
|
||||
[428(x1)] | = |
x1 +
|
||||
[434(x1)] | = |
x1 +
|
||||
[45(x1)] | = |
x1 +
|
||||
[411(x1)] | = |
x1 +
|
||||
[417(x1)] | = |
x1 +
|
||||
[423(x1)] | = |
x1 +
|
||||
[429(x1)] | = |
x1 +
|
||||
[435(x1)] | = |
x1 +
|
||||
[30(x1)] | = |
x1 +
|
||||
[36(x1)] | = |
x1 +
|
||||
[312(x1)] | = |
x1 +
|
||||
[318(x1)] | = |
x1 +
|
||||
[324(x1)] | = |
x1 +
|
||||
[330(x1)] | = |
x1 +
|
||||
[31(x1)] | = |
x1 +
|
||||
[37(x1)] | = |
x1 +
|
||||
[313(x1)] | = |
x1 +
|
||||
[319(x1)] | = |
x1 +
|
||||
[325(x1)] | = |
x1 +
|
||||
[331(x1)] | = |
x1 +
|
||||
[32(x1)] | = |
x1 +
|
||||
[38(x1)] | = |
x1 +
|
||||
[314(x1)] | = |
x1 +
|
||||
[320(x1)] | = |
x1 +
|
||||
[326(x1)] | = |
x1 +
|
||||
[332(x1)] | = |
x1 +
|
||||
[33(x1)] | = |
x1 +
|
||||
[39(x1)] | = |
x1 +
|
||||
[315(x1)] | = |
x1 +
|
||||
[321(x1)] | = |
x1 +
|
||||
[327(x1)] | = |
x1 +
|
||||
[333(x1)] | = |
x1 +
|
||||
[34(x1)] | = |
x1 +
|
||||
[310(x1)] | = |
x1 +
|
||||
[316(x1)] | = |
x1 +
|
||||
[322(x1)] | = |
x1 +
|
||||
[328(x1)] | = |
x1 +
|
||||
[334(x1)] | = |
x1 +
|
||||
[35(x1)] | = |
x1 +
|
||||
[311(x1)] | = |
x1 +
|
||||
[317(x1)] | = |
x1 +
|
||||
[323(x1)] | = |
x1 +
|
||||
[329(x1)] | = |
x1 +
|
||||
[335(x1)] | = |
x1 +
|
||||
[20(x1)] | = |
x1 +
|
||||
[26(x1)] | = |
x1 +
|
||||
[212(x1)] | = |
x1 +
|
||||
[218(x1)] | = |
x1 +
|
||||
[224(x1)] | = |
x1 +
|
||||
[230(x1)] | = |
x1 +
|
||||
[21(x1)] | = |
x1 +
|
||||
[27(x1)] | = |
x1 +
|
||||
[213(x1)] | = |
x1 +
|
||||
[219(x1)] | = |
x1 +
|
||||
[225(x1)] | = |
x1 +
|
||||
[231(x1)] | = |
x1 +
|
||||
[22(x1)] | = |
x1 +
|
||||
[28(x1)] | = |
x1 +
|
||||
[214(x1)] | = |
x1 +
|
||||
[220(x1)] | = |
x1 +
|
||||
[226(x1)] | = |
x1 +
|
||||
[232(x1)] | = |
x1 +
|
||||
[23(x1)] | = |
x1 +
|
||||
[29(x1)] | = |
x1 +
|
||||
[215(x1)] | = |
x1 +
|
||||
[221(x1)] | = |
x1 +
|
||||
[227(x1)] | = |
x1 +
|
||||
[233(x1)] | = |
x1 +
|
||||
[24(x1)] | = |
x1 +
|
||||
[210(x1)] | = |
x1 +
|
||||
[216(x1)] | = |
x1 +
|
||||
[222(x1)] | = |
x1 +
|
||||
[228(x1)] | = |
x1 +
|
||||
[234(x1)] | = |
x1 +
|
||||
[25(x1)] | = |
x1 +
|
||||
[211(x1)] | = |
x1 +
|
||||
[217(x1)] | = |
x1 +
|
||||
[223(x1)] | = |
x1 +
|
||||
[229(x1)] | = |
x1 +
|
||||
[235(x1)] | = |
x1 +
|
||||
[10(x1)] | = |
x1 +
|
||||
[16(x1)] | = |
x1 +
|
||||
[112(x1)] | = |
x1 +
|
||||
[118(x1)] | = |
x1 +
|
||||
[124(x1)] | = |
x1 +
|
||||
[130(x1)] | = |
x1 +
|
||||
[11(x1)] | = |
x1 +
|
||||
[17(x1)] | = |
x1 +
|
||||
[113(x1)] | = |
x1 +
|
||||
[119(x1)] | = |
x1 +
|
||||
[125(x1)] | = |
x1 +
|
||||
[131(x1)] | = |
x1 +
|
||||
[12(x1)] | = |
x1 +
|
||||
[18(x1)] | = |
x1 +
|
||||
[114(x1)] | = |
x1 +
|
||||
[120(x1)] | = |
x1 +
|
||||
[126(x1)] | = |
x1 +
|
||||
[132(x1)] | = |
x1 +
|
||||
[13(x1)] | = |
x1 +
|
||||
[19(x1)] | = |
x1 +
|
||||
[115(x1)] | = |
x1 +
|
||||
[121(x1)] | = |
x1 +
|
||||
[127(x1)] | = |
x1 +
|
||||
[133(x1)] | = |
x1 +
|
||||
[14(x1)] | = |
x1 +
|
||||
[110(x1)] | = |
x1 +
|
||||
[116(x1)] | = |
x1 +
|
||||
[122(x1)] | = |
x1 +
|
||||
[128(x1)] | = |
x1 +
|
||||
[134(x1)] | = |
x1 +
|
||||
[15(x1)] | = |
x1 +
|
||||
[111(x1)] | = |
x1 +
|
||||
[117(x1)] | = |
x1 +
|
||||
[123(x1)] | = |
x1 +
|
||||
[129(x1)] | = |
x1 +
|
||||
[135(x1)] | = |
x1 +
|
||||
[00(x1)] | = |
x1 +
|
||||
[06(x1)] | = |
x1 +
|
||||
[012(x1)] | = |
x1 +
|
||||
[018(x1)] | = |
x1 +
|
||||
[024(x1)] | = |
x1 +
|
||||
[030(x1)] | = |
x1 +
|
||||
[01(x1)] | = |
x1 +
|
||||
[07(x1)] | = |
x1 +
|
||||
[013(x1)] | = |
x1 +
|
||||
[019(x1)] | = |
x1 +
|
||||
[025(x1)] | = |
x1 +
|
||||
[031(x1)] | = |
x1 +
|
||||
[02(x1)] | = |
x1 +
|
||||
[08(x1)] | = |
x1 +
|
||||
[014(x1)] | = |
x1 +
|
||||
[020(x1)] | = |
x1 +
|
||||
[026(x1)] | = |
x1 +
|
||||
[032(x1)] | = |
x1 +
|
||||
[03(x1)] | = |
x1 +
|
||||
[09(x1)] | = |
x1 +
|
||||
[015(x1)] | = |
x1 +
|
||||
[021(x1)] | = |
x1 +
|
||||
[027(x1)] | = |
x1 +
|
||||
[033(x1)] | = |
x1 +
|
||||
[04(x1)] | = |
x1 +
|
||||
[010(x1)] | = |
x1 +
|
||||
[016(x1)] | = |
x1 +
|
||||
[022(x1)] | = |
x1 +
|
||||
[028(x1)] | = |
x1 +
|
||||
[034(x1)] | = |
x1 +
|
||||
[05(x1)] | = |
x1 +
|
||||
[011(x1)] | = |
x1 +
|
||||
[017(x1)] | = |
x1 +
|
||||
[023(x1)] | = |
x1 +
|
||||
[029(x1)] | = |
x1 +
|
||||
[035(x1)] | = |
x1 +
|
There are 51840 ruless (increase limit for explicit display).
There are no rules in the TRS. Hence, it is terminating.