/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
0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
0(1(2(x1))) -> 0(2(1(1(x1))))
0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
2(3(1(x1))) -> 3(4(2(1(x1))))
2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 0#(2(3(1(3(x1))))) -> 0#(3(4(2(1(3(x1))))))
 0#(2(3(1(3(x1))))) -> 2#(1(3(x1)))
 0#(2(3(1(3(x1))))) -> 3#(4(2(1(3(x1)))))
 0#(2(3(1(3(x1))))) -> 4#(2(1(3(x1))))
 0#(1(0(2(2(x1))))) -> 0#(0(2(1(4(2(x1))))))
 0#(1(0(2(2(x1))))) -> 0#(2(1(4(2(x1)))))
 0#(1(0(2(2(x1))))) -> 2#(1(4(2(x1))))
 0#(1(0(2(2(x1))))) -> 4#(2(x1))
 0#(1(2(0(x1)))) -> 0#(2(1(1(0(x1)))))
 0#(1(2(0(x1)))) -> 2#(1(1(0(x1))))
 0#(5(2(0(4(x1))))) -> 0#(4(2(5(0(4(x1))))))
 0#(5(2(0(4(x1))))) -> 2#(5(0(4(x1))))
 0#(5(2(0(4(x1))))) -> 4#(2(5(0(4(x1)))))
 2#(0(1(3(1(x1))))) -> 0#(2(x1))
 2#(0(1(3(1(x1))))) -> 2#(x1)
 2#(0(1(3(1(x1))))) -> 3#(0(2(x1)))
 2#(0(1(3(1(x1))))) -> 4#(3(0(2(x1))))
 2#(0(1(3(5(x1))))) -> 0#(3(x1))
 2#(0(1(3(5(x1))))) -> 2#(5(1(1(0(3(x1))))))
 2#(0(1(3(5(x1))))) -> 3#(x1)
 2#(0(1(5(3(x1))))) -> 0#(5(x1))
 2#(0(1(5(3(x1))))) -> 2#(1(1(3(0(5(x1))))))
 2#(0(1(5(3(x1))))) -> 3#(0(5(x1)))
 2#(3(2(0(x1)))) -> 2#(2(1(3(0(x1)))))
 2#(3(2(0(x1)))) -> 2#(1(3(0(x1))))
 2#(3(2(0(x1)))) -> 3#(0(x1))
 3#(0(1(2(0(x1))))) -> 0#(2(1(0(x1))))
 3#(0(1(2(0(x1))))) -> 2#(1(0(x1)))
 3#(0(1(2(0(x1))))) -> 3#(4(0(2(1(0(x1))))))
 3#(0(1(2(0(x1))))) -> 4#(0(2(1(0(x1)))))
 3#(2(0(1(0(x1))))) -> 0#(0(x1))
 3#(2(0(1(0(x1))))) -> 2#(1(5(0(0(x1)))))
 3#(2(0(1(0(x1))))) -> 3#(2(1(5(0(0(x1))))))
 3#(5(3(1(3(x1))))) -> 3#(5(4(3(1(3(x1))))))
 3#(5(3(1(3(x1))))) -> 4#(3(1(3(x1))))
 4#(5(3(2(x1)))) -> 2#(5(4(x1)))
 4#(5(3(2(x1)))) -> 3#(4(2(5(4(x1)))))
 4#(5(3(2(x1)))) -> 4#(2(5(4(x1))))
 4#(5(3(2(x1)))) -> 4#(x1)
-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))

Problem 1: 

SCC Processor:
-> Pairs:
 0#(2(3(1(3(x1))))) -> 0#(3(4(2(1(3(x1))))))
 0#(2(3(1(3(x1))))) -> 2#(1(3(x1)))
 0#(2(3(1(3(x1))))) -> 3#(4(2(1(3(x1)))))
 0#(2(3(1(3(x1))))) -> 4#(2(1(3(x1))))
 0#(1(0(2(2(x1))))) -> 0#(0(2(1(4(2(x1))))))
 0#(1(0(2(2(x1))))) -> 0#(2(1(4(2(x1)))))
 0#(1(0(2(2(x1))))) -> 2#(1(4(2(x1))))
 0#(1(0(2(2(x1))))) -> 4#(2(x1))
 0#(1(2(0(x1)))) -> 0#(2(1(1(0(x1)))))
 0#(1(2(0(x1)))) -> 2#(1(1(0(x1))))
 0#(5(2(0(4(x1))))) -> 0#(4(2(5(0(4(x1))))))
 0#(5(2(0(4(x1))))) -> 2#(5(0(4(x1))))
 0#(5(2(0(4(x1))))) -> 4#(2(5(0(4(x1)))))
 2#(0(1(3(1(x1))))) -> 0#(2(x1))
 2#(0(1(3(1(x1))))) -> 2#(x1)
 2#(0(1(3(1(x1))))) -> 3#(0(2(x1)))
 2#(0(1(3(1(x1))))) -> 4#(3(0(2(x1))))
 2#(0(1(3(5(x1))))) -> 0#(3(x1))
 2#(0(1(3(5(x1))))) -> 2#(5(1(1(0(3(x1))))))
 2#(0(1(3(5(x1))))) -> 3#(x1)
 2#(0(1(5(3(x1))))) -> 0#(5(x1))
 2#(0(1(5(3(x1))))) -> 2#(1(1(3(0(5(x1))))))
 2#(0(1(5(3(x1))))) -> 3#(0(5(x1)))
 2#(3(2(0(x1)))) -> 2#(2(1(3(0(x1)))))
 2#(3(2(0(x1)))) -> 2#(1(3(0(x1))))
 2#(3(2(0(x1)))) -> 3#(0(x1))
 3#(0(1(2(0(x1))))) -> 0#(2(1(0(x1))))
 3#(0(1(2(0(x1))))) -> 2#(1(0(x1)))
 3#(0(1(2(0(x1))))) -> 3#(4(0(2(1(0(x1))))))
 3#(0(1(2(0(x1))))) -> 4#(0(2(1(0(x1)))))
 3#(2(0(1(0(x1))))) -> 0#(0(x1))
 3#(2(0(1(0(x1))))) -> 2#(1(5(0(0(x1)))))
 3#(2(0(1(0(x1))))) -> 3#(2(1(5(0(0(x1))))))
 3#(5(3(1(3(x1))))) -> 3#(5(4(3(1(3(x1))))))
 3#(5(3(1(3(x1))))) -> 4#(3(1(3(x1))))
 4#(5(3(2(x1)))) -> 2#(5(4(x1)))
 4#(5(3(2(x1)))) -> 3#(4(2(5(4(x1)))))
 4#(5(3(2(x1)))) -> 4#(2(5(4(x1))))
 4#(5(3(2(x1)))) -> 4#(x1)
-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 4#(5(3(2(x1)))) -> 4#(x1)
->->-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))
->->Cycle:
->->-> Pairs:
 2#(0(1(3(1(x1))))) -> 2#(x1)
->->-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 4#(5(3(2(x1)))) -> 4#(x1)
-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))
->Projection:
 pi(4#) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 2#(0(1(3(1(x1))))) -> 2#(x1)
-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))
->Projection:
 pi(2#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0(2(0(1(x1)))) -> 0(0(2(4(1(x1)))))
 0(2(3(1(3(x1))))) -> 0(3(4(2(1(3(x1))))))
 0(4(1(5(2(x1))))) -> 0(4(2(5(1(1(x1))))))
 0(1(0(2(2(x1))))) -> 0(0(2(1(4(2(x1))))))
 0(1(0(3(1(x1))))) -> 0(3(4(0(1(1(x1))))))
 0(1(2(0(x1)))) -> 0(0(2(1(1(x1)))))
 0(1(2(0(x1)))) -> 0(2(1(1(0(x1)))))
 0(1(2(4(x1)))) -> 4(0(2(1(1(x1)))))
 0(1(2(1(x1)))) -> 0(2(1(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(2(5(1(1(x1)))))
 0(1(2(5(x1)))) -> 0(4(2(1(5(x1)))))
 0(1(2(x1))) -> 0(2(1(1(x1))))
 0(1(3(1(x1)))) -> 0(0(3(1(1(x1)))))
 0(1(3(1(x1)))) -> 3(0(2(1(1(1(x1))))))
 0(1(4(1(x1)))) -> 4(0(1(1(1(x1)))))
 0(1(4(5(1(x1))))) -> 4(0(2(5(1(1(x1))))))
 0(1(4(5(x1)))) -> 0(4(1(1(5(x1)))))
 0(1(5(0(1(x1))))) -> 0(0(1(5(5(1(x1))))))
 0(5(2(0(4(x1))))) -> 0(4(2(5(0(4(x1))))))
 0(5(3(2(5(x1))))) -> 0(4(3(5(2(5(x1))))))
 0(5(3(2(x1)))) -> 0(3(4(2(5(x1)))))
 0(5(3(1(5(x1))))) -> 5(0(3(4(1(5(x1))))))
 0(5(3(1(x1)))) -> 5(0(3(1(1(1(x1))))))
 0(5(1(3(2(x1))))) -> 3(0(2(1(1(5(x1))))))
 2(0(1(3(1(x1))))) -> 1(1(4(3(0(2(x1))))))
 2(0(1(3(5(x1))))) -> 2(5(1(1(0(3(x1))))))
 2(0(1(5(3(x1))))) -> 2(1(1(3(0(5(x1))))))
 2(3(2(0(x1)))) -> 2(2(1(3(0(x1)))))
 2(3(1(0(1(x1))))) -> 0(3(2(1(1(5(x1))))))
 2(3(1(4(1(x1))))) -> 3(4(2(5(1(1(x1))))))
 2(3(1(x1))) -> 3(4(2(1(x1))))
 2(3(5(1(2(x1))))) -> 2(3(2(1(5(1(x1))))))
 2(4(5(2(x1)))) -> 2(1(4(2(5(x1)))))
 3(0(1(2(0(x1))))) -> 3(4(0(2(1(0(x1))))))
 3(0(1(2(x1)))) -> 3(4(0(2(1(x1)))))
 3(2(0(1(0(x1))))) -> 3(2(1(5(0(0(x1))))))
 3(2(3(5(1(x1))))) -> 3(3(4(2(1(5(x1))))))
 3(5(3(1(3(x1))))) -> 3(5(4(3(1(3(x1))))))
 4(0(3(3(1(x1))))) -> 0(3(4(3(1(1(x1))))))
 4(4(3(2(5(x1))))) -> 3(4(2(4(1(5(x1))))))
 4(4(3(2(x1)))) -> 4(3(4(2(1(x1)))))
 4(5(0(5(2(x1))))) -> 0(4(2(1(5(5(x1))))))
 4(5(2(3(1(x1))))) -> 5(3(4(3(2(1(x1))))))
 4(5(2(5(2(x1))))) -> 4(2(5(5(2(1(x1))))))
 4(5(3(2(x1)))) -> 3(4(2(5(4(x1)))))
 4(5(3(2(x1)))) -> 3(5(4(2(1(x1)))))
 4(5(3(1(x1)))) -> 3(5(4(4(1(x1)))))
 4(5(3(1(x1)))) -> 4(3(1(5(1(x1)))))
 4(5(3(5(1(x1))))) -> 4(5(5(4(3(1(x1))))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.