/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
add(x,0) -> x
add(x,s(y)) -> s(add(x,y))
quad(x) -> z | add(x,x) -> y, add(y,y) -> z
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 ADD(x,s(y)) -> ADD(x,y)
-> QPairs:
 Empty
-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z

Conditional Termination Problem 2:
-> Pairs:
 QUAD(x) -> ADD(x,x)
 QUAD(x) -> ADD(y,y) | add(x,x) -> y
-> QPairs:
 ADD(x,s(y)) -> ADD(x,y)
-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 ADD(x,s(y)) -> ADD(x,y)
-> QPairs:
 Empty
-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ADD(x,s(y)) -> ADD(x,y)
->->-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z

Problem 1.1: 

Conditional Subterm Processor:
-> Pairs:
 ADD(x,s(y)) -> ADD(x,y)
-> QPairs:
 Empty
-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z
->Projection:
 pi(ADD) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 QUAD(x) -> ADD(x,x)
 QUAD(x) -> ADD(y,y) | add(x,x) -> y
-> QPairs:
 ADD(x,s(y)) -> ADD(x,y)
-> Rules:
 add(x,0) -> x
 add(x,s(y)) -> s(add(x,y))
 quad(x) -> z | add(x,x) -> y, add(y,y) -> z
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.