/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 x:S y:S)
(RULES
f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
g(s(x:S)) -> x:S
h(s(x:S)) -> x:S
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 F(x:S,y:S) -> G(s(x:S)) | c(g(x:S)) ->* c(a)
 F(x:S,y:S) -> H(s(x:S)) | c(h(x:S)) ->* c(a)
-> QPairs:
 Empty
-> Rules:
 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S

Conditional Termination Problem 2:
-> Pairs:
 F(x:S,y:S) -> G(x:S)
 F(x:S,y:S) -> H(x:S)
-> QPairs:
 Empty
-> Rules:
 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 F(x:S,y:S) -> G(s(x:S)) | c(g(x:S)) ->* c(a)
 F(x:S,y:S) -> H(s(x:S)) | c(h(x:S)) ->* c(a)
-> QPairs:
 Empty
-> Rules:
 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 F(x:S,y:S) -> G(x:S)
 F(x:S,y:S) -> H(x:S)
-> QPairs:
 Empty
-> Rules:
 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.