TRS Equational pair #487092707

details

property	value
status	complete
benchmark	AC07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.28301 seconds
cpu usage	5.03375
user time	4.8446
system time	0.189149
max virtual memory	1.827784E7
max residence set size	272536.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) RRRPoloETRSProof [EQUIVALENT, 160 ms]
(2) ETRS
(3) RRRPoloETRSProof [EQUIVALENT, 45 ms]
(4) ETRS
(5) EquationalDependencyPairsProof [EQUIVALENT, 0 ms]
(6) EDP
(7) EDependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) EDP
        (10) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (11) EDP
        (12) EUsableRulesReductionPairsProof [EQUIVALENT, 4 ms]
        (13) EDP
        (14) PisEmptyProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) EDP
        (17) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (18) EDP
        (19) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (20) EDP
        (21) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) EDP
        (26) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (27) EDP
        (28) ERuleRemovalProof [EQUIVALENT, 0 ms]
        (29) EDP
        (30) EDPPoloProof [EQUIVALENT, 0 ms]
        (31) EDP
        (32) PisEmptyProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) EDP
        (35) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (36) EDP
        (37) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (38) EDP
        (39) PisEmptyProof [EQUIVALENT, 0 ms]
        (40) YES


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

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

   sum(x, y) -> S(int(x, y))
   S(nil) -> 0
   S(cons(x, xs)) -> plus(x, S(xs))
   plus(x, 0) -> x
   plus(x, s(y)) -> s(plus(x, y))
   int(0, 0) -> cons(0, nil)
   int(0, s(y)) -> cons(0, int(s(0), s(y)))
   int(s(x), 0) -> nil
   int(s(x), s(y)) -> intlist(int(x, y))
   intlist(nil) -> nil
   intlist(cons(x, y)) -> cons(s(x), intlist(y))

The set E consists of the following equations:

   plus(x, y) == plus(y, x)
   plus(plus(x, y), z) == plus(x, plus(y, z))


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

(1) RRRPoloETRSProof (EQUIVALENT)
The following E TRS is given: Equational rewrite system:
The TRS R consists of the following rules:

   sum(x, y) -> S(int(x, y))
   S(nil) -> 0
   S(cons(x, xs)) -> plus(x, S(xs))
   plus(x, 0) -> x
   plus(x, s(y)) -> s(plus(x, y))
   int(0, 0) -> cons(0, nil)
   int(0, s(y)) -> cons(0, int(s(0), s(y)))
   int(s(x), 0) -> nil
   int(s(x), s(y)) -> intlist(int(x, y))
   intlist(nil) -> nil
   intlist(cons(x, y)) -> cons(s(x), intlist(y))

The set E consists of the following equations:

   plus(x, y) == plus(y, x)
   plus(plus(x, y), z) == plus(x, plus(y, z))

The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering:

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Equational