Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/188674)

The rewrite relation of the following TRS is considered.

There are 180 ruless (increase limit for explicit display).

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
0
[4(x1)] = x1 +
0
[3(x1)] = x1 +
1
[2(x1)] = x1 +
2/3
[1(x1)] = x1 +
2/3
[0(x1)] = x1 +
2/3
all of the following rules can be deleted.

There are 169 ruless (increase limit for explicit display).

1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) (181)
1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (182)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) (183)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) (184)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 5(1(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))))) (185)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (186)
3(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) (187)
3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 2(2(5(2(3(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))))))) (188)
3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) (189)
3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) (190)
0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) (191)

1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(5(3(1(3(1(3(5(0(x1))))))))) (192)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) (193)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(5(0(x1))) (194)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(1(3(5(0(x1))))) (195)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(1(3(1(3(5(0(x1))))))) (196)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 1#(3(5(0(x1)))) (197)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 1#(3(1(3(5(0(x1)))))) (198)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 3#(4(1(1(3(1(2(3(x1)))))))) (199)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 3#(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) (200)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 3#(1(2(3(x1)))) (201)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(3(1(2(3(x1))))) (202)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1))))))))))))))) (203)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(2(3(x1))) (204)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(1(3(1(2(3(x1)))))) (205)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(x1) (206)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(5(3(2(0(1(x1)))))) (207)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(4(2(4(2(3(5(3(2(0(1(x1))))))))))) (208)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(4(1(1(3(1(2(3(x1)))))))) (209)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))) (210)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(2(0(1(x1)))) (211)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) (212)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(1(2(3(x1)))) (213)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(3(1(2(3(x1))))) (214)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1))))))))))))))) (215)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(2(3(x1))) (216)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(1(3(1(2(3(x1)))))) (217)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 0#(1(x1)) (218)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 3#(5(2(0(x1)))) (219)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 3#(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))) (220)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 1#(0(4(5(2(4(3(5(2(0(x1)))))))))) (221)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 0#(4(5(2(4(3(5(2(0(x1))))))))) (222)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 0#(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) (223)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(5(3(1(3(1(3(5(0(x1))))))))) (224)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) (225)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(5(0(x1))) (226)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(3(1(1(2(1(5(3(5(0(x1)))))))))) (227)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(2(4(4(4(0(3(0(x1)))))))) (228)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))) (229)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(1(3(5(0(x1))))) (230)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(1(3(1(3(5(0(x1))))))) (231)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(1(1(2(1(5(3(5(0(x1))))))))) (232)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(0(5(4(2(3(2(4(4(4(0(3(0(x1))))))))))))) (233)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(5(3(5(0(x1))))) (234)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))) (235)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(3(5(0(x1)))) (236)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(3(1(3(5(0(x1)))))) (237)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(2(1(5(3(5(0(x1))))))) (238)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1))))))))))))))) (239)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(1(2(1(5(3(5(0(x1)))))))) (240)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) (241)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1))))))))))))))) (242)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))) (243)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(5(2(2(0(4(5(2(2(5(x1)))))))))) (244)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(4(5(2(2(5(x1)))))) (245)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(3(3(1(1(2(1(5(3(5(0(x1))))))))))) (246)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(3(0(x1))) (247)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))) (248)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))))) (249)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(0(5(2(2(0(4(5(2(2(5(x1))))))))))) (250)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (251)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 3#(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))) (252)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(5(2(2(0(4(5(2(2(5(x1)))))))))) (253)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(4(5(2(2(5(x1)))))) (254)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))))) (255)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(0(5(2(2(0(4(5(2(2(5(x1))))))))))) (256)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (257)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 3#(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))) (258)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 3#(1(1(2(4(1(4(5(2(5(4(x1))))))))))) (259)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 1#(4(5(2(5(4(x1)))))) (260)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 1#(2(4(1(4(5(2(5(4(x1))))))))) (261)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 1#(1(2(4(1(4(5(2(5(4(x1)))))))))) (262)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 0#(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) (263)

1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
2
[4(x1)] = x1 +
2
[3(x1)] = x1 +
2
[2(x1)] = x1 +
2
[1(x1)] = x1 +
2
[0(x1)] = x1 +
2
[3#(x1)] = x1 +
1
[1#(x1)] = x1 +
2
[0#(x1)] = x1 +
0
together with the usable rules
1(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 0(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) (181)
1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (182)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) (183)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) (184)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 5(1(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))))) (185)
1(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (186)
3(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) (187)
3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 2(2(5(2(3(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))))))) (188)
3(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) (189)
3(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 3(1(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1)))))))))))))))) (190)
0(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 0(5(3(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))))) (191)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(5(3(1(3(1(3(5(0(x1))))))))) (192)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(5(0(x1))) (194)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(1(3(5(0(x1))))) (195)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 3#(1(3(1(3(5(0(x1))))))) (196)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 1#(3(5(0(x1)))) (197)
3#(3(3(0(4(2(1(4(4(4(2(0(2(0(5(0(x1)))))))))))))))) → 1#(3(1(3(5(0(x1)))))) (198)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 3#(4(1(1(3(1(2(3(x1)))))))) (199)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 3#(1(2(3(x1)))) (201)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(3(1(2(3(x1))))) (202)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1))))))))))))))) (203)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(2(3(x1))) (204)
3#(0(5(1(0(3(0(4(3(0(5(3(4(3(4(3(x1)))))))))))))))) → 1#(1(3(1(2(3(x1)))))) (205)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(x1) (206)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(5(3(2(0(1(x1)))))) (207)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(4(2(4(2(3(5(3(2(0(1(x1))))))))))) (208)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(4(1(1(3(1(2(3(x1)))))))) (209)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(3(4(2(4(2(3(5(3(2(0(1(x1)))))))))))) (210)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(2(0(1(x1)))) (211)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 3#(1(2(3(x1)))) (213)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(3(1(2(3(x1))))) (214)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(2(4(5(4(2(2(3(4(1(1(3(1(2(3(x1))))))))))))))) (215)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(2(3(x1))) (216)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 1#(1(3(1(2(3(x1)))))) (217)
3#(0(2(3(5(0(1(0(5(5(4(3(1(2(3(1(x1)))))))))))))))) → 0#(1(x1)) (218)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 3#(5(2(0(x1)))) (219)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 3#(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))) (220)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 1#(0(4(5(2(4(3(5(2(0(x1)))))))))) (221)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 0#(4(5(2(4(3(5(2(0(x1))))))))) (222)
1#(5(4(3(5(5(4(0(4(3(1(2(0(1(0(0(x1)))))))))))))))) → 0#(4(3(2(2(4(1(0(4(5(2(4(3(5(2(0(x1)))))))))))))))) (223)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(5(3(1(3(1(3(5(0(x1))))))))) (224)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(5(2(4(5(5(2(3(5(3(1(3(1(3(5(0(x1)))))))))))))))) (225)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(5(0(x1))) (226)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(3(1(1(2(1(5(3(5(0(x1)))))))))) (227)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(2(4(4(4(0(3(0(x1)))))))) (228)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))) (229)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(1(3(5(0(x1))))) (230)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(1(3(1(3(5(0(x1))))))) (231)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(1(1(2(1(5(3(5(0(x1))))))))) (232)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 3#(0(5(4(2(3(2(4(4(4(0(3(0(x1))))))))))))) (233)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(5(3(5(0(x1))))) (234)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(4(5(0(3(3(1(1(2(1(5(3(5(0(x1)))))))))))))) (235)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(3(5(0(x1)))) (236)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(3(1(3(5(0(x1)))))) (237)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(2(1(5(3(5(0(x1))))))) (238)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(1(4(5(0(3(3(1(1(2(1(5(3(5(0(x1))))))))))))))) (239)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(1(2(1(5(3(5(0(x1)))))))) (240)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 1#(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1))))))))))))))) (242)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))) (243)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(5(2(2(0(4(5(2(2(5(x1)))))))))) (244)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(4(5(2(2(5(x1)))))) (245)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(3(3(1(1(2(1(5(3(5(0(x1))))))))))) (246)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(3(0(x1))) (247)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))) (248)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))))) (249)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(0(5(2(2(0(4(5(2(2(5(x1))))))))))) (250)
1#(4(3(2(4(3(5(4(2(0(1(4(0(1(3(0(x1)))))))))))))))) → 0#(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (251)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 3#(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))) (252)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(5(2(2(0(4(5(2(2(5(x1)))))))))) (253)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(4(5(2(2(5(x1)))))) (254)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1))))))))))))))) (255)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(0(5(2(2(0(4(5(2(2(5(x1))))))))))) (256)
1#(1(0(3(0(5(4(2(3(2(4(4(4(0(3(0(x1)))))))))))))))) → 0#(0(2(3(2(0(0(5(2(2(0(4(5(2(2(5(x1)))))))))))))))) (257)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 3#(4(2(3(1(1(2(4(1(4(5(2(5(4(x1)))))))))))))) (258)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 3#(1(1(2(4(1(4(5(2(5(4(x1))))))))))) (259)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 1#(4(5(2(5(4(x1)))))) (260)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 1#(2(4(1(4(5(2(5(4(x1))))))))) (261)
0#(5(0(3(2(4(2(5(1(0(5(3(5(4(2(4(x1)))))))))))))))) → 1#(1(2(4(1(4(5(2(5(4(x1)))))))))) (262)
and no rules could be deleted.

1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.