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

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

Problem 1: 

Dependency Pairs Processor:

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

Conditional Termination Problem 2:
-> Pairs:
 SUB(s(z),s(y)) -> SUB(z,y)
-> QPairs:
 Empty
-> Rules:
 sub(s(z),s(y)) -> x | sub(z,y) -> x
 sub(z,0) -> z


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 SUB(s(z),s(y)) -> SUB(z,y)
-> QPairs:
 Empty
-> Rules:
 sub(s(z),s(y)) -> x | sub(z,y) -> x
 sub(z,0) -> z
->Projection:
 pi(SUB) = 1

Problem 1.2: 

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

The problem is finite.