The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

(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(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(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(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(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(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(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(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(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(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Tuples:

0'(0(z0)) → c1(0'(z0))
0'(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(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(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(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(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(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))))))))))))))))))))))))))))), 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3'(4(5(z0))) → c3(3'(5(z0)))
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0'(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))), 0'(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))), 0'(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))), 0'(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))), 0'(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))), 0'(1(0(1(0(0(1(1(1(1(0(z0))))))))))), 0'(1(0(0(1(1(1(1(0(z0))))))))), 0'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 0'(z0))

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(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(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))))))))))))))))))))))))))))), 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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(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(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))), 0'(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))))))), 0'(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))))))), 0'(0(1(0(1(0(1(0(0(1(1(1(1(0(z0)))))))))))))), 0'(1(0(1(0(1(0(0(1(1(1(1(0(z0))))))))))))), 0'(1(0(1(0(0(1(1(1(1(0(z0))))))))))), 0'(1(0(0(1(1(1(1(0(z0))))))))), 0'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 0'(z0))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

0(z0) → 1(z0)
0(0(z0)) → 0(z0)
0(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(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(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(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(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(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(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(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(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(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(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(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))