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(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(0(1(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(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(0(1(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(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → c3(1'(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1'(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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))))))))))))))), 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(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)))
2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(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))))))))))))))), 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(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))
2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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(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))))))))))))))), 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(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(0(1(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(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(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(1(0(0(1(1(1(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(1(0(1(1(1(1(1(1(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(0(1(1(1(1(1(1(0(0(0(1(0(1(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(1(1(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(1(0(1(1(1(0(0(1(1(0(1(1(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(1(0(0(0(0(0(0(0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(1(1(0(0(0(1(0(1(1(1(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(0(1(1(1(0(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(1(1(0(1(1(1(0(0(0(1(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(0(1(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(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))