TRS Conditional pair #487563003

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	n099.star.cs.uiowa.edu
space	Mixed_CTRS_2014

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	120.831574917 seconds
cpu usage	120.672165916
max memory	4.5776896E7

stage attributes

key	value
output-size	28867
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 v_NonEmpty:S x:S y:S)
(RULES
a -> h(b)
a -> h(c)
f(x:S) -> y:S | a ->* h(y:S)
g(x:S,b) -> g(f(c),x:S) | f(b) ->* x:S, x:S ->* c
)

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

Problem 1: 

Dependency Pairs Processor:

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

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

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