TRS Equat 89423 pair #381732682

details

property	value
status	complete
benchmark	maude2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n094.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.71270298958 seconds
cpu usage	6.498616661
max memory	3.06036736E8

stage attributes

key	value
output-size	27486
starexec-result	MAYBE

output

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


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


MAYBE
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given ETRS could not be shown:

(0) ETRS
(1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms]
(2) EDP
(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) EDP
        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
        (7) EDP
        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 10 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) EUsableRulesProof [EQUIVALENT, 0 ms]
        (23) EDP
    (24) EDP
    (25) EDP
    (26) EDP


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

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

   p(s(N)) -> N
   +(N, 0) -> N
   +(s(N), s(M)) -> s(s(+(N, M)))
   *(N, 0) -> 0
   *(s(N), s(M)) -> s(+(N, +(M, *(N, M))))
   gt(0, M) -> False
   gt(NzN, 0) -> u_4(is_NzNat(NzN))
   u_4(True) -> True
   is_NzNat(0) -> False
   is_NzNat(s(N)) -> True
   gt(s(N), s(M)) -> gt(N, M)
   lt(N, M) -> gt(M, N)
   d(0, N) -> N
   d(s(N), s(M)) -> d(N, M)
   quot(N, NzM) -> u_11(is_NzNat(NzM), N, NzM)
   u_11(True, N, NzM) -> u_1(gt(N, NzM), N, NzM)
   u_1(True, N, NzM) -> s(quot(d(N, NzM), NzM))
   quot(NzM, NzM) -> u_01(is_NzNat(NzM))
   u_01(True) -> s(0)
   quot(N, NzM) -> u_21(is_NzNat(NzM), NzM, N)
   u_21(True, NzM, N) -> u_2(gt(NzM, N))
   u_2(True) -> 0
   gcd(0, N) -> 0
   gcd(NzM, NzM) -> u_02(is_NzNat(NzM), NzM)
   u_02(True, NzM) -> NzM
   gcd(NzN, NzM) -> u_31(is_NzNat(NzN), is_NzNat(NzM), NzN, NzM)
   u_31(True, True, NzN, NzM) -> u_3(gt(NzN, NzM), NzN, NzM)
   u_3(True, NzN, NzM) -> gcd(d(NzN, NzM), NzM)

The set E consists of the following equations:

   *(x, y) == *(y, x)
   +(x, y) == +(y, x)
   d(x, y) == d(y, x)
   gcd(x, y) == gcd(y, x)


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

(1) EquationalDependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:
The TRS P consists of the following rules:

   +^1(s(N), s(M)) -> +^1(N, M)
   *^1(s(N), s(M)) -> +^1(N, +(M, *(N, M)))
   *^1(s(N), s(M)) -> +^1(M, *(N, M))
   *^1(s(N), s(M)) -> *^1(N, M)
   GT(NzN, 0) -> U_4(is_NzNat(NzN))
   GT(NzN, 0) -> IS_NZNAT(NzN)
   GT(s(N), s(M)) -> GT(N, M)
   LT(N, M) -> GT(M, N)

popout

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

job log

popout

actions all output return to TRS Equat 89423