/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)
(RULES
cond(true,x) -> cond(odd(x),p(x))
odd(0) -> false
odd(s(0)) -> true
odd(s(s(x))) -> odd(x)
p(0) -> 0
p(s(x)) -> x
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 COND(true,x) -> COND(odd(x),p(x))
 COND(true,x) -> ODD(x)
 COND(true,x) -> P(x)
 ODD(s(s(x))) -> ODD(x)
-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 COND(true,x) -> COND(odd(x),p(x))
 COND(true,x) -> ODD(x)
 COND(true,x) -> P(x)
 ODD(s(s(x))) -> ODD(x)
-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ODD(s(s(x))) -> ODD(x)
->->-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
->->Cycle:
->->-> Pairs:
 COND(true,x) -> COND(odd(x),p(x))
->->-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ODD(s(s(x))) -> ODD(x)
-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
->Projection:
 pi(ODD) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pairs Processor:
-> Pairs:
 COND(true,x) -> COND(odd(x),p(x))
-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
-> Usable rules:
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[odd](X) = 1/2.X
[p](X) = 1/2.X + 1/2
[0] = 1/2
[false] = 0
[s](X) = 2.X + 1
[true] = 1
[COND](X1,X2) = 1/2.X1 + 1/2.X2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 cond(true,x) -> cond(odd(x),p(x))
 odd(0) -> false
 odd(s(0)) -> true
 odd(s(s(x))) -> odd(x)
 p(0) -> 0
 p(s(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.