TRS_Equational 2019-03-21 05.09 pair #429997276

details

property	value
status	complete
benchmark	AC47.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	Mixed_AC_and_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.92329 seconds
cpu usage	7.03364
user time	6.78782
system time	0.245814
max virtual memory	1.8277816E7
max residence set size	531188.0

stage attributes

key	value
starexec-result	YES

output

6.94/2.87	YES
6.94/2.88	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
6.94/2.88	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.94/2.88	
6.94/2.88	
6.94/2.88	Termination of the given ETRS could be proven:
6.94/2.88	
6.94/2.88	(0) ETRS
6.94/2.88	(1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms]
6.94/2.88	(2) EDP
6.94/2.88	(3) EDependencyGraphProof [EQUIVALENT, 2 ms]
6.94/2.88	(4) AND
6.94/2.88	    (5) EDP
6.94/2.88	        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
6.94/2.88	        (7) EDP
6.94/2.88	        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
6.94/2.88	        (9) EDP
6.94/2.88	        (10) PisEmptyProof [EQUIVALENT, 0 ms]
6.94/2.88	        (11) YES
6.94/2.88	    (12) EDP
6.94/2.88	        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
6.94/2.88	        (14) EDP
6.94/2.88	        (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
6.94/2.88	        (16) EDP
6.94/2.88	        (17) PisEmptyProof [EQUIVALENT, 0 ms]
6.94/2.88	        (18) YES
6.94/2.88	    (19) EDP
6.94/2.88	        (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
6.94/2.88	        (21) EDP
6.94/2.88	        (22) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
6.94/2.88	        (23) EDP
6.94/2.88	        (24) PisEmptyProof [EQUIVALENT, 0 ms]
6.94/2.88	        (25) YES
6.94/2.88	    (26) EDP
6.94/2.88	        (27) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
6.94/2.88	        (28) EDP
6.94/2.88	        (29) EDPPoloProof [EQUIVALENT, 19 ms]
6.94/2.88	        (30) EDP
6.94/2.88	        (31) EDependencyGraphProof [EQUIVALENT, 0 ms]
6.94/2.88	        (32) EDP
6.94/2.88	        (33) EDPPoloProof [EQUIVALENT, 0 ms]
6.94/2.88	        (34) EDP
6.94/2.88	        (35) EDependencyGraphProof [EQUIVALENT, 0 ms]
6.94/2.88	        (36) TRUE
6.94/2.88	
6.94/2.88	
6.94/2.88	----------------------------------------
6.94/2.88	
6.94/2.88	(0)
6.94/2.88	Obligation:
6.94/2.88	Equational rewrite system:
6.94/2.88	The TRS R consists of the following rules:
6.94/2.88	
6.94/2.88	   eq(0, 0) -> true
6.94/2.88	   eq(0, s(x)) -> false
6.94/2.88	   eq(s(x), 0) -> false
6.94/2.88	   eq(s(x), s(y)) -> eq(x, y)
6.94/2.88	   or(true, y) -> true
6.94/2.88	   or(false, y) -> y
6.94/2.88	   union(empty, h) -> h
6.94/2.88	   union(edge(x, y, i), h) -> edge(x, y, union(i, h))
6.94/2.88	   reach(x, y, empty, h) -> false
6.94/2.88	   reach(x, y, edge(u, v, i), h) -> if_reach_1(eq(x, u), x, y, edge(u, v, i), h)
6.94/2.88	   if_reach_1(true, x, y, edge(u, v, i), h) -> if_reach_2(eq(y, v), x, y, edge(u, v, i), h)
6.94/2.88	   if_reach_1(false, x, y, edge(u, v, i), h) -> reach(x, y, i, edge(u, v, h))
6.94/2.88	   if_reach_2(true, x, y, edge(u, v, i), h) -> true
6.94/2.88	   if_reach_2(false, x, y, edge(u, v, i), h) -> or(reach(x, y, i, h), reach(v, y, union(i, h), empty))
6.94/2.88	
6.94/2.88	The set E consists of the following equations:
6.94/2.88	
6.94/2.88	   eq(x, y) == eq(y, x)
6.94/2.88	   or(x, y) == or(y, x)
6.94/2.88	   or(or(x, y), z) == or(x, or(y, z))
6.94/2.88	
6.94/2.88	
6.94/2.88	----------------------------------------
6.94/2.88	
6.94/2.88	(1) EquationalDependencyPairsProof (EQUIVALENT)
6.94/2.88	Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:
6.94/2.88	The TRS P consists of the following rules:
6.94/2.88	
6.94/2.88	   EQ(s(x), s(y)) -> EQ(x, y)
6.94/2.88	   UNION(edge(x, y, i), h) -> UNION(i, h)
6.94/2.88	   REACH(x, y, edge(u, v, i), h) -> IF_REACH_1(eq(x, u), x, y, edge(u, v, i), h)
6.94/2.88	   REACH(x, y, edge(u, v, i), h) -> EQ(x, u)
6.94/2.88	   IF_REACH_1(true, x, y, edge(u, v, i), h) -> IF_REACH_2(eq(y, v), x, y, edge(u, v, i), h)
6.94/2.88	   IF_REACH_1(true, x, y, edge(u, v, i), h) -> EQ(y, v)
6.94/2.88	   IF_REACH_1(false, x, y, edge(u, v, i), h) -> REACH(x, y, i, edge(u, v, h))
6.94/2.88	   IF_REACH_2(false, x, y, edge(u, v, i), h) -> OR(reach(x, y, i, h), reach(v, y, union(i, h), empty))
6.94/2.88	   IF_REACH_2(false, x, y, edge(u, v, i), h) -> REACH(x, y, i, h)
6.94/2.88	   IF_REACH_2(false, x, y, edge(u, v, i), h) -> REACH(v, y, union(i, h), empty)
6.94/2.88	   IF_REACH_2(false, x, y, edge(u, v, i), h) -> UNION(i, h)
6.94/2.88	   OR(or(true, y), ext) -> OR(true, ext)
6.94/2.88	
6.94/2.88	The TRS R consists of the following rules:
6.94/2.88	
6.94/2.88	   eq(0, 0) -> true
6.94/2.88	   eq(0, s(x)) -> false
6.94/2.88	   eq(s(x), 0) -> false
6.94/2.88	   eq(s(x), s(y)) -> eq(x, y)

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actions all output return to TRS_Equational 2019-03-21 05.09