TRS Standard pair #516965576

details

property	value
status	complete
benchmark	jw18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n003.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.447968959808 seconds
cpu usage	0.359067141
max memory	6807552.0

stage attributes

key	value
output-size	1618
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)
(RULES
f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a))
-> Rules:
 f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))

Problem 1: 

SCC Processor:
-> Pairs:
 F(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a))
-> Rules:
 f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a))
->->-> Rules:
 f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a))
-> Rules:
 f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))
-> Usable rules:
 f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))
->Interpretation type:
 Simple mixed
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 1/2.X1.X2 + 1/2.X2
[a] = 1/2
[fSNonEmpty] = 0
[F](X1,X2) = 1/2.X1.X2 + 1/2.X1 + 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

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