/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
a -> c
a -> d
b -> c
b -> d
f(x,y) -> y | s(x) -> t(y)
g(x,x) -> h(x,x)
s(k) -> t(a)
s(l) -> t(a)
)

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

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 S(k) -> A
 S(l) -> A
-> QPairs:
 Empty
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 f(x,y) -> y | s(x) -> t(y)
 g(x,x) -> h(x,x)
 s(k) -> t(a)
 s(l) -> t(a)

Conditional Termination Problem 2:
-> Pairs:
 F(x,y) -> S(x)
-> QPairs:
 S(k) -> A
 S(l) -> A
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 f(x,y) -> y | s(x) -> t(y)
 g(x,x) -> h(x,x)
 s(k) -> t(a)
 s(l) -> t(a)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 S(k) -> A
 S(l) -> A
-> QPairs:
 Empty
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 f(x,y) -> y | s(x) -> t(y)
 g(x,x) -> h(x,x)
 s(k) -> t(a)
 s(l) -> t(a)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 F(x,y) -> S(x)
-> QPairs:
 S(k) -> A
 S(l) -> A
-> Rules:
 a -> c
 a -> d
 b -> c
 b -> d
 f(x,y) -> y | s(x) -> t(y)
 g(x,x) -> h(x,x)
 s(k) -> t(a)
 s(l) -> t(a)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.