/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
#(#(x1)) -> #(x1)
#(0(x1)) -> 0(#(x1))
#(1(x1)) -> 1(#(x1))
#($(x1)) -> *($(x1))
#(*(x1)) -> *(x1)
0(*(x1)) -> *(1(x1))
1(*(x1)) -> 0(#(x1))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ##(0(x1)) -> ##(x1)
 ##(0(x1)) -> 0#(#(x1))
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))

Problem 1: 

SCC Processor:
-> Pairs:
 ##(0(x1)) -> ##(x1)
 ##(0(x1)) -> 0#(#(x1))
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ##(0(x1)) -> ##(x1)
 ##(0(x1)) -> 0#(#(x1))
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
->->-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ##(0(x1)) -> ##(x1)
 ##(0(x1)) -> 0#(#(x1))
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
-> Usable rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[#](X) = 2.X + 2
[0](X) = 2.X + 2
[1](X) = 2.X + 2
[$](X) = 2.X + 2
[*](X) = 2.X + 2
[##](X) = 2.X + 1
[0#](X) = X + 1
[1#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 ##(0(x1)) -> 0#(#(x1))
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ##(0(x1)) -> 0#(#(x1))
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
->->-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ##(0(x1)) -> 0#(#(x1))
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
-> Usable rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[#](X) = 2.X + 1
[0](X) = 2.X + 1
[1](X) = 2.X + 1
[$](X) = 2.X + 2
[*](X) = 2.X + 1
[##](X) = 2.X + 2
[0#](X) = X + 2
[1#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
->->-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ##(1(x1)) -> ##(x1)
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
-> Usable rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[#](X) = X + 2
[0](X) = X + 2
[1](X) = X + 2
[$](X) = 2.X + 1
[*](X) = X + 2
[##](X) = 2.X + 2
[0#](X) = 2.X + 2
[1#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
->->-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ##(1(x1)) -> 1#(#(x1))
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
-> Usable rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[#](X) = 2.X + 1
[0](X) = 2.X + 1
[1](X) = 2.X + 1
[$](X) = X
[*](X) = 2.X + 1
[##](X) = 2.X + 2
[0#](X) = 2.X + 1
[1#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> ##(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> 0#(#(x1))
->->-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(*(x1)) -> 1#(x1)
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
-> Usable rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[#](X) = 2.X + 2
[0](X) = 2.X + 2
[1](X) = 2.X + 2
[$](X) = X + 2
[*](X) = 2.X + 2
[0#](X) = 2.X + 2
[1#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 1#(*(x1)) -> 0#(#(x1))
-> Rules:
 #(#(x1)) -> #(x1)
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(*(x1)) -> *(x1)
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.