/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 v_NonEmpty:S m:S n:S r:S)
(RULES
p(m:S,0,0) -> m:S
p(m:S,s(n:S),0) -> p(0,n:S,m:S)
p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 P(m:S,s(n:S),0) -> P(0,n:S,m:S)
 P(m:S,n:S,s(r:S)) -> P(m:S,r:S,n:S)
-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)

Problem 1: 

SCC Processor:
-> Pairs:
 P(m:S,s(n:S),0) -> P(0,n:S,m:S)
 P(m:S,n:S,s(r:S)) -> P(m:S,r:S,n:S)
-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 P(m:S,s(n:S),0) -> P(0,n:S,m:S)
 P(m:S,n:S,s(r:S)) -> P(m:S,r:S,n:S)
->->-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 P(m:S,s(n:S),0) -> P(0,n:S,m:S)
 P(m:S,n:S,s(r:S)) -> P(m:S,r:S,n:S)
-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X1,X2,X3) = 0
[0] = 1
[fSNonEmpty] = 0
[s](X) = 2.X + 2
[P](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3

Problem 1: 

SCC Processor:
-> Pairs:
 P(m:S,n:S,s(r:S)) -> P(m:S,r:S,n:S)
-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 P(m:S,n:S,s(r:S)) -> P(m:S,r:S,n:S)
->->-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 P(m:S,n:S,s(r:S)) -> P(m:S,r:S,n:S)
-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X1,X2,X3) = 0
[0] = 0
[fSNonEmpty] = 0
[s](X) = 2.X + 2
[P](X1,X2,X3) = 2.X2 + 2.X3

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 p(m:S,0,0) -> m:S
 p(m:S,s(n:S),0) -> p(0,n:S,m:S)
 p(m:S,n:S,s(r:S)) -> p(m:S,r:S,n:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.