TRS Condi 20667 pair #381733054

details

property	value
status	complete
benchmark	jlap09-ex17.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n087.star.cs.uiowa.edu
space	Mixed_CTRS_2014

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	6.68387293816 seconds
cpu usage	6.558533916
max memory	5.8949632E7

stage attributes

key	value
output-size	5820
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR x y)
(RULES
a -> h(b)
a -> h(c)
f(x) -> y | a -> h(y)
g(x,b) -> g(f(c),x) | f(b) -> x, x -> c
)

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

Problem 1: 

Dependency Pairs Processor:

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

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 G(x,b) -> F(c) | f(b) -> x, x -> c
 G(x,b) -> G(f(c),x) | f(b) -> x, x -> c
-> QPairs:
 Empty
-> Rules:
 a -> h(b)
 a -> h(c)
 f(x) -> y | a -> h(y)
 g(x,b) -> g(f(c),x) | f(b) -> x, x -> c
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(x,b) -> G(f(c),x) | f(b) -> x, x -> c
->->-> Rules:
 a -> h(b)
 a -> h(c)
 f(x) -> y | a -> h(y)
 g(x,b) -> g(f(c),x) | f(b) -> x, x -> c

Problem 1.1: 

Simplification and Narrowing on Condition Processor:
-> Pairs:
 G(x,b) -> G(f(c),x) | f(b) -> x, x -> c
-> QPairs:
 Empty
-> Rules:
 a -> h(b)
 a -> h(c)
 f(x) -> y | a -> h(y)
 g(x,b) -> g(f(c),x) | f(b) -> x, x -> c
->Narrowed Pairs:
->->Original Pair:
 G(x,b) -> G(f(c),x) | f(b) -> x, x -> c
->-> Narrowed pairs:
 G(f(b),b) -> G(f(c),f(b)) | f(b) -> c
 G(x2,b) -> G(f(c),x2) | a -> h(b), b -> x2, x2 -> c

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