Integ TRS Inner 43557 pair #381740665

details

property	value
status	complete
benchmark	24.itrs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n038.star.cs.uiowa.edu
space	Mixed_ITRS_2014

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.59102106094 seconds
cpu usage	6.49142563
max memory	3.24427776E8

stage attributes

key	value
output-size	103875
starexec-result	YES

output

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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given ITRS could be proven:

(0) ITRS
(1) ITRStoIDPProof [EQUIVALENT, 0 ms]
(2) IDP
(3) UsableRulesProof [EQUIVALENT, 0 ms]
(4) IDP
(5) IDPNonInfProof [SOUND, 357 ms]
(6) AND
    (7) IDP
        (8) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (9) AND
            (10) IDP
                (11) IDPNonInfProof [SOUND, 20 ms]
                (12) IDP
                (13) IDependencyGraphProof [EQUIVALENT, 0 ms]
                (14) TRUE
            (15) IDP
                (16) IDPNonInfProof [SOUND, 85 ms]
                (17) AND
                    (18) IDP
                        (19) IDependencyGraphProof [EQUIVALENT, 0 ms]
                        (20) TRUE
                    (21) IDP
                        (22) IDependencyGraphProof [EQUIVALENT, 0 ms]
                        (23) IDP
                        (24) IDPNonInfProof [SOUND, 0 ms]
                        (25) IDP
                        (26) IDependencyGraphProof [EQUIVALENT, 0 ms]
                        (27) TRUE
    (28) IDP
        (29) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (30) IDP
        (31) IDPNonInfProof [SOUND, 24 ms]
        (32) IDP
        (33) IDependencyGraphProof [EQUIVALENT, 0 ms]
        (34) TRUE


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

(0)
Obligation:
ITRS problem:

The following function symbols are pre-defined:
<<<
 & 	~ 	Bwand: (Integer, Integer) -> Integer
 >= 	~ 	Ge: (Integer, Integer) -> Boolean
 | 	~ 	Bwor: (Integer, Integer) -> Integer
 / 	~ 	Div: (Integer, Integer) -> Integer
 != 	~ 	Neq: (Integer, Integer) -> Boolean
 && 	~ 	Land: (Boolean, Boolean) -> Boolean
 ! 	~ 	Lnot: (Boolean) -> Boolean
 = 	~ 	Eq: (Integer, Integer) -> Boolean
 <= 	~ 	Le: (Integer, Integer) -> Boolean
 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
 % 	~ 	Mod: (Integer, Integer) -> Integer
 > 	~ 	Gt: (Integer, Integer) -> Boolean
 + 	~ 	Add: (Integer, Integer) -> Integer
 -1 	~ 	UnaryMinus: (Integer) -> Integer
 < 	~ 	Lt: (Integer, Integer) -> Boolean
 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
 - 	~ 	Sub: (Integer, Integer) -> Integer
 ~ 	~ 	Bwnot: (Integer) -> Integer
 * 	~ 	Mul: (Integer, Integer) -> Integer
>>>

The TRS R consists of the following rules:
eval_1(x, y) -> Cond_eval_1(x > 0 && y > 0 && x > y, x, y)
Cond_eval_1(TRUE, x, y) -> eval_2(x, y)
eval_1(x, y) -> Cond_eval_11(x > 0 && y > 0 && y >= x, x, y)
Cond_eval_11(TRUE, x, y) -> eval_3(x, y)
eval_2(x, y) -> Cond_eval_2(x > 0, x, y)
Cond_eval_2(TRUE, x, y) -> eval_2(x - 1, y)
eval_2(x, y) -> Cond_eval_21(0 >= x, x, y)
Cond_eval_21(TRUE, x, y) -> eval_1(x, y)
eval_3(x, y) -> Cond_eval_3(y > 0, x, y)
Cond_eval_3(TRUE, x, y) -> eval_3(x, y - 1)
eval_3(x, y) -> Cond_eval_31(0 >= y, x, y)
Cond_eval_31(TRUE, x, y) -> eval_1(x, y)
The set Q consists of the following terms:
eval_1(x0, x1)
Cond_eval_1(TRUE, x0, x1)
Cond_eval_11(TRUE, x0, x1)
eval_2(x0, x1)
Cond_eval_2(TRUE, x0, x1)
Cond_eval_21(TRUE, x0, x1)
eval_3(x0, x1)

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