(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

0(x1) → 1(x1)
0(0(x1)) → 0(x1)
3(4(5(x1))) → 4(3(5(x1)))
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(1(1(0(0(1(1(0(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(1(0(0(1(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(0(0(0(1(0(0(0(0(1(0(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(0(1(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0(0(0(1(0(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(1(1(1(1(0(1(1(1(1(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(0(1(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(1(1(1(1(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

0(z0) → 1(z0)
0(0(z0)) → 0(z0)
0(0(0(1(0(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(1(1(1(1(0(1(1(1(1(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(0(1(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(1(1(1(1(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
3(4(5(z0))) → 4(3(5(z0)))
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(1(1(0(0(1(1(0(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(1(0(0(1(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(0(0(0(1(0(0(0(0(1(0(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(0(1(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Tuples:

0'(0(z0)) → c1(0'(z0))
0'(0(0(1(0(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(1(1(1(1(0(1(1(1(1(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(0(1(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(1(1(1(1(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → c2(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 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3'(4(5(z0))) → c3(3'(5(z0)))
2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 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0'(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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0'(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))), 0'(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))), 0'(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))), 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S tuples:

0'(0(z0)) → c1(0'(z0))
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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 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3'(4(5(z0))) → c3(3'(5(z0)))
2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 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K tuples:none
Defined Rule Symbols:

0, 3, 2

Defined Pair Symbols:

0', 3', 2'

Compound Symbols:

c1, c2, c3, c4

(3) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

0'(0(z0)) → c1(0'(z0))
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0'(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))), 0'(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))), 0'(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))))), 0'(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))), 0'(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))))), 0'(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))), 0'(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))))))))))))), 0'(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))), 0'(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))), 0'(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))), 0'(0(0(0(1(0(1(0(0(0(0(0(z0)))))))))))), 0'(0(0(1(0(1(0(0(0(0(0(z0))))))))))), 0'(0(1(0(1(0(0(0(0(0(z0)))))))))), 0'(1(0(1(0(0(0(0(0(z0))))))))), 0'(1(0(0(0(0(0(z0))))))), 0'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

0(z0) → 1(z0)
0(0(z0)) → 0(z0)
0(0(0(1(0(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(1(1(1(1(0(1(1(1(1(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(0(1(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(1(1(1(1(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
3(4(5(z0))) → 4(3(5(z0)))
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(1(1(0(0(1(1(0(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(1(0(0(1(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(0(0(0(1(0(0(0(0(1(0(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(0(1(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Tuples:

3'(4(5(z0))) → c3(3'(5(z0)))
S tuples:

3'(4(5(z0))) → c3(3'(5(z0)))
K tuples:none
Defined Rule Symbols:

0, 3, 2

Defined Pair Symbols:

3'

Compound Symbols:

c3

(5) CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication transformation)

Removed 1 of 1 dangling nodes:

3'(4(5(z0))) → c3(3'(5(z0)))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

0(z0) → 1(z0)
0(0(z0)) → 0(z0)
0(0(0(1(0(1(0(1(0(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(0(1(0(0(1(1(1(1(0(1(1(1(1(1(1(1(1(0(0(1(0(0(1(0(0(0(0(1(0(0(0(1(0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(0(1(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(1(1(0(0(1(1(0(1(1(0(0(0(0(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(1(0(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(0(0(1(1(1(1(1(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(0(0(0(1(1(0(1(1(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(1(1(0(1(1(1(0(0(0(1(1(1(1(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(1(1(1(1(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
3(4(5(z0))) → 4(3(5(z0)))
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(1(1(0(0(1(1(0(1(1(1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(1(0(0(1(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(0(1(0(1(1(0(1(1(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(0(0(0(1(0(0(0(0(1(0(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(0(1(0(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(0(1(0(0(1(0(1(0(1(1(1(1(0(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(0(1(1(1(1(0(1(1(1(1(1(0(0(1(1(0(0(1(1(1(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(0(1(0(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

0, 3, 2

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(8) BOUNDS(O(1), O(1))