/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 v_NonEmpty:S x:S y:S)
(RULES
average(0,0) -> 0
average(0,s(0)) -> 0
average(0,s(s(0))) -> s(0)
average(s(x:S),y:S) -> average(x:S,s(y:S))
average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AVERAGE(s(x:S),y:S) -> AVERAGE(x:S,s(y:S))
 AVERAGE(x:S,s(s(s(y:S)))) -> AVERAGE(s(x:S),y:S)
-> Rules:
 average(0,0) -> 0
 average(0,s(0)) -> 0
 average(0,s(s(0))) -> s(0)
 average(s(x:S),y:S) -> average(x:S,s(y:S))
 average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))

Problem 1: 

SCC Processor:
-> Pairs:
 AVERAGE(s(x:S),y:S) -> AVERAGE(x:S,s(y:S))
 AVERAGE(x:S,s(s(s(y:S)))) -> AVERAGE(s(x:S),y:S)
-> Rules:
 average(0,0) -> 0
 average(0,s(0)) -> 0
 average(0,s(s(0))) -> s(0)
 average(s(x:S),y:S) -> average(x:S,s(y:S))
 average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AVERAGE(s(x:S),y:S) -> AVERAGE(x:S,s(y:S))
 AVERAGE(x:S,s(s(s(y:S)))) -> AVERAGE(s(x:S),y:S)
->->-> Rules:
 average(0,0) -> 0
 average(0,s(0)) -> 0
 average(0,s(s(0))) -> s(0)
 average(s(x:S),y:S) -> average(x:S,s(y:S))
 average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 AVERAGE(s(x:S),y:S) -> AVERAGE(x:S,s(y:S))
 AVERAGE(x:S,s(s(s(y:S)))) -> AVERAGE(s(x:S),y:S)
-> Rules:
 average(0,0) -> 0
 average(0,s(0)) -> 0
 average(0,s(s(0))) -> s(0)
 average(s(x:S),y:S) -> average(x:S,s(y:S))
 average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[s](X) = X + 2
[AVERAGE](X1,X2) = 2.X1 + X2

Problem 1: 

SCC Processor:
-> Pairs:
 AVERAGE(x:S,s(s(s(y:S)))) -> AVERAGE(s(x:S),y:S)
-> Rules:
 average(0,0) -> 0
 average(0,s(0)) -> 0
 average(0,s(s(0))) -> s(0)
 average(s(x:S),y:S) -> average(x:S,s(y:S))
 average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AVERAGE(x:S,s(s(s(y:S)))) -> AVERAGE(s(x:S),y:S)
->->-> Rules:
 average(0,0) -> 0
 average(0,s(0)) -> 0
 average(0,s(s(0))) -> s(0)
 average(s(x:S),y:S) -> average(x:S,s(y:S))
 average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 AVERAGE(x:S,s(s(s(y:S)))) -> AVERAGE(s(x:S),y:S)
-> Rules:
 average(0,0) -> 0
 average(0,s(0)) -> 0
 average(0,s(s(0))) -> s(0)
 average(s(x:S),y:S) -> average(x:S,s(y:S))
 average(x:S,s(s(s(y:S)))) -> s(average(s(x:S),y:S))
->Projection:
 pi(AVERAGE) = 2

Problem 1: 

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

The problem is finite.