TRS Standard pair #487068489

details

property	value
status	complete
benchmark	z06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n189.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	2.25577 seconds
cpu usage	1.98095
user time	1.41946
system time	0.561491
max virtual memory	706804.0
max residence set size	7900.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 F(b,f(a,x:S)) -> F(b,f(b,f(b,x:S)))
 F(b,f(a,x:S)) -> F(b,f(b,x:S))
 F(b,f(a,x:S)) -> F(b,x:S)
-> Rules:
 f(a,f(b,x:S)) -> f(a,f(a,f(a,x:S)))
 f(b,f(a,x:S)) -> f(b,f(b,f(b,x:S)))
-> Usable rules:
 f(a,f(b,x:S)) -> f(a,f(a,f(a,x:S)))
 f(b,f(a,x:S)) -> f(b,f(b,f(b,x:S)))
->Mace4 Output:
 ============================== Mace4 =================================
Mace4 (64) version 2009-11A, November 2009.
Process 45729 was started by sandbox2 on n189.star.cs.uiowa.edu,
Mon Jun 22 00:51:24 2020
The command was "./mace4 -c -f /tmp/mace49398195822001100545.in".
============================== end of head ===========================

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

% Reading from file /tmp/mace49398195822001100545.in

assign(max_seconds,20).

formulas(assumptions).
gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility).
gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility).
arrow_s0(x1,y) -> arrow_s0(f2(x1,x2),f2(y,x2)) # label(congruence).
arrow_s0(x2,y) -> arrow_s0(f2(x1,x2),f2(x1,y)) # label(congruence).
arrow_s0(x1,y) -> arrow_s0(f7(x1,x2),f7(y,x2)) # label(congruence).
arrow_s0(x2,y) -> arrow_s0(f7(x1,x2),f7(x1,y)) # label(congruence).
arrow_s0(x1,y) -> arrow_s0(f8(x1,x2),f8(y,x2)) # label(congruence).
arrow_s0(x2,y) -> arrow_s0(f8(x1,x2),f8(x1,y)) # label(congruence).
arrow_s0(f2(f3,f2(f4,x1)),f2(f3,f2(f3,f2(f3,x1)))) # label(replacement).
arrow_s0(f2(f4,f2(f3,x1)),f2(f4,f2(f4,f2(f4,x1)))) # label(replacement).
arrow_s0(f8(x2,x3),x2) # label(replacement).
arrow_s0(f8(x2,x3),x3) # label(replacement).
arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion).

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