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

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

Problem 1: 

Dependency Pairs Processor:

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

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

The problem is finite.