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


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YES

Problem 1: 

(VAR x1)
(RULES
0(2(1(2(x1)))) -> 0(2(2(1(5(x1)))))
0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1))))))
0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1))))))
0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1))))))
0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1))))))
0(1(2(x1))) -> 0(2(1(0(x1))))
0(1(2(x1))) -> 0(2(4(1(5(x1)))))
0(1(2(x1))) -> 0(1(3(4(2(3(x1))))))
0(1(2(x1))) -> 0(3(2(1(0(x1)))))
0(1(2(x1))) -> 1(0(2(3(x1))))
0(1(2(x1))) -> 1(0(3(2(3(x1)))))
0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1))))))
0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1))))))
0(1(3(1(x1)))) -> 5(0(3(1(1(x1)))))
0(1(5(1(x1)))) -> 5(0(3(1(1(x1)))))
0(5(2(x1))) -> 0(2(4(5(3(x1)))))
0(5(2(x1))) -> 5(4(2(3(0(4(x1))))))
0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1))))))
0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1))))))
2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1))))))
2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1))))))
2(0(1(x1))) -> 0(2(2(3(4(1(x1))))))
2(0(1(x1))) -> 0(2(1(1(4(x1)))))
2(0(1(x1))) -> 0(3(2(3(1(1(x1))))))
2(0(1(x1))) -> 0(3(2(4(1(x1)))))
2(0(1(x1))) -> 3(0(2(1(4(x1)))))
2(0(1(x1))) -> 3(0(2(1(x1))))
2(0(1(x1))) -> 4(0(4(2(1(4(x1))))))
2(0(4(1(x1)))) -> 3(0(2(4(1(x1)))))
2(0(5(1(x1)))) -> 5(4(2(1(0(x1)))))
2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1))))))
2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1))))))
2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1))))))
2(4(0(1(x1)))) -> 1(0(2(4(4(x1)))))
2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1))))))
2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1))))))
2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1))))))
2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1))))))
2(5(2(0(1(x1))))) -> 0(2(4(1(5(2(x1))))))
2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1))))))
2(5(1(x1))) -> 0(2(1(5(1(x1)))))
2(5(1(x1))) -> 1(4(5(4(2(x1)))))
2(5(1(x1))) -> 1(5(0(2(4(1(x1))))))
2(5(1(x1))) -> 5(0(2(1(4(x1)))))
2(5(1(x1))) -> 5(2(1(1(1(1(x1))))))
2(5(1(x1))) -> 5(2(1(4(1(x1)))))
2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1))))))
2(5(5(2(x1)))) -> 5(5(2(3(2(x1)))))
2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1))))))
)

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.