(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(x1))))))))))))) → 0(0(0(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1(1(0(0(1(1(0(1(0(0(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(0(0(0(0(1(0(0(0(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(0(1(1(0(0(0(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 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)
3(4(5(z0))) → 4(3(5(z0)))
2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))) → 0(0(0(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1(1(0(0(1(1(0(1(0(0(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(0(0(0(0(1(0(0(0(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(0(1(1(0(0(0(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))
Tuples:

0'(z0) → c(1'(z0))
0'(0(z0)) → c1(0'(z0))
3'(4(5(z0))) → c2(3'(5(z0)))
2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))) → c3(0'(0(0(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(1(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(1(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(1(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(1(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(1(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(1(1(1(0(1(0(0(1(0(0(1(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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1'(1(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(1(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 1'(1(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))), 1'(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))), 1'(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))), 1'(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))), 1'(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))), 1'(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))), 0'(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))), 0'(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))), 1'(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))), 0'(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))), 0'(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))), 1'(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))), 1'(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))), 1'(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))), 1'(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))), 0'(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))), 1'(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))), 0'(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))), 1'(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))), 0'(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))), 0'(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))), 0'(0(1(1(0(0(1(1(1(1(1(z0))))))))))), 0'(1(1(0(0(1(1(1(1(1(z0)))))))))), 1'(1(0(0(1(1(1(1(1(z0))))))))), 1'(0(0(1(1(1(1(1(z0)))))))), 0'(0(1(1(1(1(1(z0))))))), 0'(1(1(1(1(1(z0)))))), 1'(1(1(1(1(z0))))), 1'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
1'(1(0(0(1(1(0(1(0(0(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(0(0(0(0(1(0(0(0(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(0(1(1(0(0(0(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → c4(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(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0))
S tuples:

0'(z0) → c(1'(z0))
0'(0(z0)) → c1(0'(z0))
3'(4(5(z0))) → c2(3'(5(z0)))
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1'(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))), 1'(0(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))), 1'(1(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))))), 1'(1(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))), 1'(1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))))), 1'(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))))), 0'(0(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))))), 0'(1(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))))), 1'(0(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))), 0'(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))), 0'(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))), 1'(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))), 1'(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))), 1'(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))), 1'(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))), 0'(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))), 1'(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))), 0'(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))), 1'(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))), 0'(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))), 0'(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))), 0'(0(1(1(0(0(1(1(1(1(1(z0))))))))))), 0'(1(1(0(0(1(1(1(1(1(z0)))))))))), 1'(1(0(0(1(1(1(1(1(z0))))))))), 1'(0(0(1(1(1(1(1(z0)))))))), 0'(0(1(1(1(1(1(z0))))))), 0'(1(1(1(1(1(z0)))))), 1'(1(1(1(1(z0))))), 1'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
1'(1(0(0(1(1(0(1(0(0(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(0(0(0(0(1(0(0(0(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(0(1(1(0(0(0(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → c4(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(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0))
K tuples:none
Defined Rule Symbols:

0, 3, 2, 1

Defined Pair Symbols:

0', 3', 2', 1'

Compound Symbols:

c, 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(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))))), 0'(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))), 0'(0(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))))), 0'(0(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))), 1'(1(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))))), 1'(1(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))))), 1'(1(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))))), 1'(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))))), 0'(1(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))))), 1'(0(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))))), 0'(1(0(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))))), 1'(0(0(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))))), 0'(0(0(0(1(1(0(0(1(1(1(1(1(z0))))))))))))), 0'(0(0(1(1(0(0(1(1(1(1(1(z0)))))))))))), 0'(0(1(1(0(0(1(1(1(1(1(z0))))))))))), 0'(1(1(0(0(1(1(1(1(1(z0)))))))))), 1'(1(0(0(1(1(1(1(1(z0))))))))), 1'(0(0(1(1(1(1(1(z0)))))))), 0'(0(1(1(1(1(1(z0))))))), 0'(1(1(1(1(1(z0)))))), 1'(1(1(1(1(z0))))), 1'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
1'(1(0(0(1(1(0(1(0(0(1(0(1(1(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(0(1(0(1(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(0(0(0(0(1(0(0(0(1(0(1(1(0(0(1(1(0(1(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(0(1(1(0(0(0(1(0(1(1(0(1(1(0(1(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → c4(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(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

0'(z0) → c(1'(z0))
3'(4(5(z0))) → c2(3'(5(z0)))
S tuples:

0'(z0) → c(1'(z0))
3'(4(5(z0))) → c2(3'(5(z0)))
K tuples:none
Defined Rule Symbols:

0, 3, 2, 1

Defined Pair Symbols:

0', 3'

Compound Symbols:

c, c2

(5) CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication transformation)

Removed 2 of 2 dangling nodes:

0'(z0) → c(1'(z0))
3'(4(5(z0))) → c2(3'(5(z0)))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

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

0, 3, 2, 1

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

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