TRS Equational pair #487092761

details

property	value
status	complete
benchmark	AC21.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.5394 seconds
cpu usage	16.0732
user time	15.4704
system time	0.602807
max virtual memory	1.8288852E7
max residence set size	1211396.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 335 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (9) EDP
        (10) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) EDP
        (15) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (16) EDP
        (17) EUsableRulesReductionPairsProof [EQUIVALENT, 5 ms]
        (18) EDP
        (19) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) EDP
        (24) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (25) EDP
        (26) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (27) EDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) EDP
        (31) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (32) EDP
        (33) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (34) EDP
        (35) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (38) YES
    (39) EDP
        (40) ESharpUsableEquationsProof [EQUIVALENT, 158 ms]
        (41) EDP
        (42) EUsableRulesReductionPairsProof [EQUIVALENT, 201 ms]
        (43) EDP
        (44) ERuleRemovalProof [EQUIVALENT, 33 ms]
        (45) EDP
        (46) EDPPoloProof [EQUIVALENT, 0 ms]
        (47) EDP
        (48) PisEmptyProof [EQUIVALENT, 0 ms]
        (49) YES
    (50) EDP
        (51) ESharpUsableEquationsProof [EQUIVALENT, 35 ms]
        (52) EDP
        (53) EDPPoloProof [EQUIVALENT, 238 ms]
        (54) EDP
        (55) EDPPoloProof [EQUIVALENT, 226 ms]
        (56) EDP
        (57) EDPPoloProof [EQUIVALENT, 211 ms]
        (58) EDP
        (59) EDPPoloProof [EQUIVALENT, 26 ms]
        (60) EDP
        (61) PisEmptyProof [EQUIVALENT, 0 ms]
        (62) YES


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

(0)
Obligation:
Equational rewrite system:
The TRS R consists of the following rules:

   0(S) -> S
   plus(S, x) -> x
   plus(0(x), 0(y)) -> 0(plus(x, y))
   plus(0(x), 1(y)) -> 1(plus(x, y))
   plus(0(x), j(y)) -> j(plus(x, y))
   plus(1(x), 1(y)) -> j(plus(1(S), plus(x, y)))
   plus(j(x), j(y)) -> 1(plus(j(S), plus(x, y)))
   plus(1(x), j(y)) -> 0(plus(x, y))
   opp(S) -> S
   opp(0(x)) -> 0(opp(x))
   opp(1(x)) -> j(opp(x))
   opp(j(x)) -> 1(opp(x))
   minus(x, y) -> plus(opp(y), x)
   times(S, x) -> S
   times(0(x), y) -> 0(times(x, y))
   times(1(x), y) -> plus(0(times(x, y)), y)
   times(j(x), y) -> minus(0(times(x, y)), y)
   sign(x) -> if_sign(x, S)
   if_sign(S, x) -> x
   if_sign(0(x), y) -> if_sign(x, y)
   if_sign(1(x), y) -> if_sign(x, 1(S))

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job log

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actions all output return to TRS Equational