TRS Equational pair #516978314

details

property	value
status	complete
benchmark	AC46.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n008.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.22806096077 seconds
cpu usage	8.90817087
max memory	5.52378368E8

stage attributes

key	value
output-size	37596
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given ETRS could be proven:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 6 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) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) EDP
        (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (14) EDP
        (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (16) EDP
        (17) PisEmptyProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) EDP
        (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (21) EDP
        (22) EDPPoloProof [EQUIVALENT, 0 ms]
        (23) EDP
        (24) PisEmptyProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) EDP
        (27) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (28) EDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) EDP
        (32) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (33) EDP
        (34) EDPPoloProof [EQUIVALENT, 11 ms]
        (35) EDP
        (36) PisEmptyProof [EQUIVALENT, 0 ms]
        (37) YES
    (38) EDP
        (39) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (40) EDP
        (41) EDPPoloProof [EQUIVALENT, 22 ms]
        (42) EDP
        (43) EDPPoloProof [EQUIVALENT, 0 ms]
        (44) EDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES


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

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

   eq(0, 0) -> true
   eq(0, s(x)) -> false
   eq(s(x), 0) -> false
   eq(s(x), s(y)) -> eq(x, y)
   le(0, y) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   app(nil, y) -> y
   app(add(n, x), y) -> add(n, app(x, y))
   min(add(n, nil)) -> n
   min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x)))
   if_min(true, add(n, add(m, x))) -> min(add(n, x))
   if_min(false, add(n, add(m, x))) -> min(add(m, x))
   rm(n, nil) -> nil
   rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x))
   if_rm(true, n, add(m, x)) -> rm(n, x)
   if_rm(false, n, add(m, x)) -> add(m, rm(n, x))
   minsort(nil, nil) -> nil
   minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y)
   if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil))
   if_minsort(false, add(n, x), y) -> minsort(x, add(n, y))

The set E consists of the following equations:

   eq(x, y) == eq(y, x)


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(1) EquationalDependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:

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job log

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actions all output return to TRS Equational