TRS Standard pair #487073474

details

property	value
status	complete
benchmark	jwteparla2.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	Waldmann_06

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	13.0821 seconds
cpu usage	13.0548
user time	11.5338
system time	1.521
max virtual memory	708856.0
max residence set size	6612.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(f(f(a,f(a,a)),a),x:S) -> F(x:S,f(x:S,a))
-> Rules:
 f(f(f(a,f(a,a)),a),x:S) -> f(x:S,f(x:S,a))
-> Usable rules:
 f(f(f(a,f(a,a)),a),x:S) -> f(x:S,f(x:S,a))
->Mace4 Output:
 ============================== Mace4 =================================
Mace4 (64) version 2009-11A, November 2009.
Process 22055 was started by sandbox2 on n178.star.cs.uiowa.edu,
Mon Jun 22 10:16:08 2020
The command was "./mace4 -c -f /tmp/mace41315634022635723058.in".
============================== end of head ===========================

============================== INPUT =================================

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