TRS Standard pair #487068474

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	n178.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	1.0578 seconds
cpu usage	0.817931
user time	0.631015
system time	0.186916
max virtual memory	706948.0
max residence set size	6184.0

stage attributes

key	value
starexec-result	YES

output

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
->Dimension:
 1
->Bound:
 4
->Interpretation:

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