/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x1)
(RULES
a12(a12(x1)) -> x1
a12(a23(a12(a23(a12(a23(x1)))))) -> x1
a12(a34(x1)) -> a34(a12(x1))
a12(a45(x1)) -> a45(a12(x1))
a12(a56(x1)) -> a56(a12(x1))
a13(a13(x1)) -> x1
a13(x1) -> a12(a23(a12(x1)))
a14(a14(x1)) -> x1
a14(x1) -> a12(a23(a34(a23(a12(x1)))))
a15(a15(x1)) -> x1
a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
a16(a16(x1)) -> x1
a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
a23(a23(x1)) -> x1
a23(a34(a23(a34(a23(a34(x1)))))) -> x1
a23(a45(x1)) -> a45(a23(x1))
a23(a56(x1)) -> a56(a23(x1))
a24(a24(x1)) -> x1
a24(x1) -> a23(a34(a23(x1)))
a25(a25(x1)) -> x1
a25(x1) -> a23(a34(a45(a34(a23(x1)))))
a26(a26(x1)) -> x1
a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
a34(a34(x1)) -> x1
a34(a45(a34(a45(a34(a45(x1)))))) -> x1
a34(a56(x1)) -> a56(a34(x1))
a35(a35(x1)) -> x1
a35(x1) -> a34(a45(a34(x1)))
a36(a36(x1)) -> x1
a36(x1) -> a34(a45(a56(a45(a34(x1)))))
a45(a45(x1)) -> x1
a45(a56(a45(a56(a45(a56(x1)))))) -> x1
a46(a46(x1)) -> x1
a46(x1) -> a45(a56(a45(x1)))
a56(a56(x1)) -> x1
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A12(a34(x1)) -> A12(x1)
 A12(a34(x1)) -> A34(a12(x1))
 A12(a45(x1)) -> A12(x1)
 A12(a45(x1)) -> A45(a12(x1))
 A12(a56(x1)) -> A12(x1)
 A12(a56(x1)) -> A56(a12(x1))
 A13(x1) -> A12(a23(a12(x1)))
 A13(x1) -> A12(x1)
 A13(x1) -> A23(a12(x1))
 A14(x1) -> A12(a23(a34(a23(a12(x1)))))
 A14(x1) -> A12(x1)
 A14(x1) -> A23(a12(x1))
 A14(x1) -> A23(a34(a23(a12(x1))))
 A14(x1) -> A34(a23(a12(x1)))
 A15(x1) -> A12(a23(a34(a45(a34(a23(a12(x1)))))))
 A15(x1) -> A12(x1)
 A15(x1) -> A23(a12(x1))
 A15(x1) -> A23(a34(a45(a34(a23(a12(x1))))))
 A15(x1) -> A34(a23(a12(x1)))
 A15(x1) -> A34(a45(a34(a23(a12(x1)))))
 A15(x1) -> A45(a34(a23(a12(x1))))
 A16(x1) -> A12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 A16(x1) -> A12(x1)
 A16(x1) -> A23(a12(x1))
 A16(x1) -> A23(a34(a45(a56(a45(a34(a23(a12(x1))))))))
 A16(x1) -> A34(a23(a12(x1)))
 A16(x1) -> A34(a45(a56(a45(a34(a23(a12(x1)))))))
 A16(x1) -> A45(a34(a23(a12(x1))))
 A16(x1) -> A45(a56(a45(a34(a23(a12(x1))))))
 A16(x1) -> A56(a45(a34(a23(a12(x1)))))
 A23(a45(x1)) -> A23(x1)
 A23(a45(x1)) -> A45(a23(x1))
 A23(a56(x1)) -> A23(x1)
 A23(a56(x1)) -> A56(a23(x1))
 A24(x1) -> A23(a34(a23(x1)))
 A24(x1) -> A23(x1)
 A24(x1) -> A34(a23(x1))
 A25(x1) -> A23(a34(a45(a34(a23(x1)))))
 A25(x1) -> A23(x1)
 A25(x1) -> A34(a23(x1))
 A25(x1) -> A34(a45(a34(a23(x1))))
 A25(x1) -> A45(a34(a23(x1)))
 A26(x1) -> A23(a34(a45(a56(a45(a34(a23(x1)))))))
 A26(x1) -> A23(x1)
 A26(x1) -> A34(a23(x1))
 A26(x1) -> A34(a45(a56(a45(a34(a23(x1))))))
 A26(x1) -> A45(a34(a23(x1)))
 A26(x1) -> A45(a56(a45(a34(a23(x1)))))
 A26(x1) -> A56(a45(a34(a23(x1))))
 A34(a56(x1)) -> A34(x1)
 A34(a56(x1)) -> A56(a34(x1))
 A35(x1) -> A34(a45(a34(x1)))
 A35(x1) -> A34(x1)
 A35(x1) -> A45(a34(x1))
 A36(x1) -> A34(a45(a56(a45(a34(x1)))))
 A36(x1) -> A34(x1)
 A36(x1) -> A45(a34(x1))
 A36(x1) -> A45(a56(a45(a34(x1))))
 A36(x1) -> A56(a45(a34(x1)))
 A46(x1) -> A45(a56(a45(x1)))
 A46(x1) -> A45(x1)
 A46(x1) -> A56(a45(x1))
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1

Problem 1: 

SCC Processor:
-> Pairs:
 A12(a34(x1)) -> A12(x1)
 A12(a34(x1)) -> A34(a12(x1))
 A12(a45(x1)) -> A12(x1)
 A12(a45(x1)) -> A45(a12(x1))
 A12(a56(x1)) -> A12(x1)
 A12(a56(x1)) -> A56(a12(x1))
 A13(x1) -> A12(a23(a12(x1)))
 A13(x1) -> A12(x1)
 A13(x1) -> A23(a12(x1))
 A14(x1) -> A12(a23(a34(a23(a12(x1)))))
 A14(x1) -> A12(x1)
 A14(x1) -> A23(a12(x1))
 A14(x1) -> A23(a34(a23(a12(x1))))
 A14(x1) -> A34(a23(a12(x1)))
 A15(x1) -> A12(a23(a34(a45(a34(a23(a12(x1)))))))
 A15(x1) -> A12(x1)
 A15(x1) -> A23(a12(x1))
 A15(x1) -> A23(a34(a45(a34(a23(a12(x1))))))
 A15(x1) -> A34(a23(a12(x1)))
 A15(x1) -> A34(a45(a34(a23(a12(x1)))))
 A15(x1) -> A45(a34(a23(a12(x1))))
 A16(x1) -> A12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 A16(x1) -> A12(x1)
 A16(x1) -> A23(a12(x1))
 A16(x1) -> A23(a34(a45(a56(a45(a34(a23(a12(x1))))))))
 A16(x1) -> A34(a23(a12(x1)))
 A16(x1) -> A34(a45(a56(a45(a34(a23(a12(x1)))))))
 A16(x1) -> A45(a34(a23(a12(x1))))
 A16(x1) -> A45(a56(a45(a34(a23(a12(x1))))))
 A16(x1) -> A56(a45(a34(a23(a12(x1)))))
 A23(a45(x1)) -> A23(x1)
 A23(a45(x1)) -> A45(a23(x1))
 A23(a56(x1)) -> A23(x1)
 A23(a56(x1)) -> A56(a23(x1))
 A24(x1) -> A23(a34(a23(x1)))
 A24(x1) -> A23(x1)
 A24(x1) -> A34(a23(x1))
 A25(x1) -> A23(a34(a45(a34(a23(x1)))))
 A25(x1) -> A23(x1)
 A25(x1) -> A34(a23(x1))
 A25(x1) -> A34(a45(a34(a23(x1))))
 A25(x1) -> A45(a34(a23(x1)))
 A26(x1) -> A23(a34(a45(a56(a45(a34(a23(x1)))))))
 A26(x1) -> A23(x1)
 A26(x1) -> A34(a23(x1))
 A26(x1) -> A34(a45(a56(a45(a34(a23(x1))))))
 A26(x1) -> A45(a34(a23(x1)))
 A26(x1) -> A45(a56(a45(a34(a23(x1)))))
 A26(x1) -> A56(a45(a34(a23(x1))))
 A34(a56(x1)) -> A34(x1)
 A34(a56(x1)) -> A56(a34(x1))
 A35(x1) -> A34(a45(a34(x1)))
 A35(x1) -> A34(x1)
 A35(x1) -> A45(a34(x1))
 A36(x1) -> A34(a45(a56(a45(a34(x1)))))
 A36(x1) -> A34(x1)
 A36(x1) -> A45(a34(x1))
 A36(x1) -> A45(a56(a45(a34(x1))))
 A36(x1) -> A56(a45(a34(x1)))
 A46(x1) -> A45(a56(a45(x1)))
 A46(x1) -> A45(x1)
 A46(x1) -> A56(a45(x1))
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A34(a56(x1)) -> A34(x1)
->->-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->->Cycle:
->->-> Pairs:
 A23(a45(x1)) -> A23(x1)
 A23(a56(x1)) -> A23(x1)
->->-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->->Cycle:
->->-> Pairs:
 A12(a34(x1)) -> A12(x1)
 A12(a45(x1)) -> A12(x1)
 A12(a56(x1)) -> A12(x1)
->->-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A34(a56(x1)) -> A34(x1)
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->Projection:
 pi(A34) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 A23(a45(x1)) -> A23(x1)
 A23(a56(x1)) -> A23(x1)
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->Projection:
 pi(A23) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 A12(a34(x1)) -> A12(x1)
 A12(a45(x1)) -> A12(x1)
 A12(a56(x1)) -> A12(x1)
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->Projection:
 pi(A12) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a12(a12(x1)) -> x1
 a12(a23(a12(a23(a12(a23(x1)))))) -> x1
 a12(a34(x1)) -> a34(a12(x1))
 a12(a45(x1)) -> a45(a12(x1))
 a12(a56(x1)) -> a56(a12(x1))
 a13(a13(x1)) -> x1
 a13(x1) -> a12(a23(a12(x1)))
 a14(a14(x1)) -> x1
 a14(x1) -> a12(a23(a34(a23(a12(x1)))))
 a15(a15(x1)) -> x1
 a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1)))))))
 a16(a16(x1)) -> x1
 a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1)))))))))
 a23(a23(x1)) -> x1
 a23(a34(a23(a34(a23(a34(x1)))))) -> x1
 a23(a45(x1)) -> a45(a23(x1))
 a23(a56(x1)) -> a56(a23(x1))
 a24(a24(x1)) -> x1
 a24(x1) -> a23(a34(a23(x1)))
 a25(a25(x1)) -> x1
 a25(x1) -> a23(a34(a45(a34(a23(x1)))))
 a26(a26(x1)) -> x1
 a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1)))))))
 a34(a34(x1)) -> x1
 a34(a45(a34(a45(a34(a45(x1)))))) -> x1
 a34(a56(x1)) -> a56(a34(x1))
 a35(a35(x1)) -> x1
 a35(x1) -> a34(a45(a34(x1)))
 a36(a36(x1)) -> x1
 a36(x1) -> a34(a45(a56(a45(a34(x1)))))
 a45(a45(x1)) -> x1
 a45(a56(a45(a56(a45(a56(x1)))))) -> x1
 a46(a46(x1)) -> x1
 a46(x1) -> a45(a56(a45(x1)))
 a56(a56(x1)) -> x1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.