TRS Standard pair #516965706

details

property	value
status	complete
benchmark	jw41.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n059.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.901058197021 seconds
cpu usage	0.80843669
max memory	8552448.0

stage attributes

key	value
output-size	2446
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(f(a,x:S),a) -> f(f(f(x:S,f(a,a)),a),a)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(f(a,x:S),a) -> f(f(f(x:S,f(a,a)),a),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(f(a,x:S),a) -> F(f(f(x:S,f(a,a)),a),a)
 F(f(a,x:S),a) -> F(f(x:S,f(a,a)),a)
-> Rules:
 f(f(a,x:S),a) -> f(f(f(x:S,f(a,a)),a),a)

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(f(a,x:S),a) -> F(f(f(x:S,f(a,a)),a),a)
 F(f(a,x:S),a) -> F(f(x:S,f(a,a)),a)
-> Rules:
 f(f(a,x:S),a) -> f(f(f(x:S,f(a,a)),a),a)
-> Usable rules:
 f(f(a,x:S),a) -> f(f(f(x:S,f(a,a)),a),a)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[f](X1,X2) = [0 1;0 0].X1 + [0 1;0 0].X2
[a] = [0;1]
[fSNonEmpty] = 0
[F](X1,X2) = [1 1;1 1].X1

Problem 1: 

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

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(f(a,x:S),a) -> F(f(f(x:S,f(a,a)),a),a)
-> Rules:
 f(f(a,x:S),a) -> f(f(f(x:S,f(a,a)),a),a)
-> Usable rules:
 f(f(a,x:S),a) -> f(f(f(x:S,f(a,a)),a),a)
->Interpretation type:
 Linear
->Coefficients:
 All rationals

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