/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 x y z)
(RULES
max(L(x)) -> x
max(N(L(0),L(y))) -> y
max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 MAX(N(L(s(x)),L(s(y)))) -> MAX(N(L(x),L(y)))
 MAX(N(L(x),N(y,z))) -> MAX(N(L(x),L(max(N(y,z)))))
 MAX(N(L(x),N(y,z))) -> MAX(N(y,z))
-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))

Problem 1: 

SCC Processor:
-> Pairs:
 MAX(N(L(s(x)),L(s(y)))) -> MAX(N(L(x),L(y)))
 MAX(N(L(x),N(y,z))) -> MAX(N(L(x),L(max(N(y,z)))))
 MAX(N(L(x),N(y,z))) -> MAX(N(y,z))
-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MAX(N(L(s(x)),L(s(y)))) -> MAX(N(L(x),L(y)))
->->-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
->->Cycle:
->->-> Pairs:
 MAX(N(L(x),N(y,z))) -> MAX(N(y,z))
->->-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pairs Processor:
-> Pairs:
 MAX(N(L(s(x)),L(s(y)))) -> MAX(N(L(x),L(y)))
-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[L](X) = 2.X
[N](X1,X2) = 2.X1 + 2.X2
[s](X) = 2.X + 2
[MAX](X) = 2.X

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 MAX(N(L(x),N(y,z))) -> MAX(N(y,z))
-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
->Projection:
 pi(MAX) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 max(L(x)) -> x
 max(N(L(0),L(y))) -> y
 max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y))))
 max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z)))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.